diff --git a/Cargo.toml b/Cargo.toml
index 5103c7802b8..c0f97e48109 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -132,6 +132,7 @@ libp2p-gossipsub = { version = "0.44.0", path = "protocols/gossipsub", optional
 [dev-dependencies]
 async-std = { version = "1.6.2", features = ["attributes"] }
 async-trait = "0.1"
+either = "1.8.0"
 env_logger = "0.10.0"
 clap = { version = "4.0.13", features = ["derive"] }
 tokio = { version = "1.15", features = ["io-util", "io-std", "macros", "rt", "rt-multi-thread"] }
diff --git a/core/CHANGELOG.md b/core/CHANGELOG.md
index a7e24f5d616..f9f293e6e38 100644
--- a/core/CHANGELOG.md
+++ b/core/CHANGELOG.md
@@ -12,11 +12,14 @@
 
 - Improve error messages in case keys cannot be decoded because of missing feature flags. See [PR 2972].
 
+- Remove `EitherError` in favor of `either::Either`. See [PR 3337].
+
 [PR 3031]: https://github.com/libp2p/rust-libp2p/pull/3031
 [PR 3058]: https://github.com/libp2p/rust-libp2p/pull/3058
 [PR 3097]: https://github.com/libp2p/rust-libp2p/pull/3097
 [PR 3090]: https://github.com/libp2p/rust-libp2p/pull/3090
 [PR 2972]: https://github.com/libp2p/rust-libp2p/pull/2972
+[PR 3337]: https://github.com/libp2p/rust-libp2p/pull/3337
 
 # 0.37.0
 
diff --git a/core/src/either.rs b/core/src/either.rs
index a34552bf28f..411251cbd84 100644
--- a/core/src/either.rs
+++ b/core/src/either.rs
@@ -24,44 +24,13 @@ use crate::{
     transport::{ListenerId, Transport, TransportError, TransportEvent},
     Multiaddr, ProtocolName,
 };
+use either::Either;
 use futures::{
     io::{IoSlice, IoSliceMut},
     prelude::*,
 };
 use pin_project::pin_project;
-use std::{fmt, io, pin::Pin, task::Context, task::Poll};
-
-#[derive(Debug, Copy, Clone)]
-pub enum EitherError<A, B> {
-    A(A),
-    B(B),
-}
-
-impl<A, B> fmt::Display for EitherError<A, B>
-where
-    A: fmt::Display,
-    B: fmt::Display,
-{
-    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-        match self {
-            EitherError::A(a) => a.fmt(f),
-            EitherError::B(b) => b.fmt(f),
-        }
-    }
-}
-
-impl<A, B> std::error::Error for EitherError<A, B>
-where
-    A: std::error::Error,
-    B: std::error::Error,
-{
-    fn source(&self) -> Option<&(dyn std::error::Error + 'static)> {
-        match self {
-            EitherError::A(a) => a.source(),
-            EitherError::B(b) => b.source(),
-        }
-    }
-}
+use std::{io, pin::Pin, task::Context, task::Poll};
 
 /// Implements `AsyncRead` and `AsyncWrite` and dispatches all method calls to
 /// either `First` or `Second`.
@@ -147,15 +116,15 @@ where
     A: TryStream<Ok = I>,
     B: TryStream<Ok = I>,
 {
-    type Item = Result<I, EitherError<A::Error, B::Error>>;
+    type Item = Result<I, Either<A::Error, B::Error>>;
 
     fn poll_next(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Option<Self::Item>> {
         match self.project() {
             EitherOutputProj::First(a) => {
-                TryStream::try_poll_next(a, cx).map(|v| v.map(|r| r.map_err(EitherError::A)))
+                TryStream::try_poll_next(a, cx).map(|v| v.map(|r| r.map_err(Either::Left)))
             }
             EitherOutputProj::Second(b) => {
-                TryStream::try_poll_next(b, cx).map(|v| v.map(|r| r.map_err(EitherError::B)))
+                TryStream::try_poll_next(b, cx).map(|v| v.map(|r| r.map_err(Either::Right)))
             }
         }
     }
@@ -166,33 +135,33 @@ where
     A: Sink<I>,
     B: Sink<I>,
 {
-    type Error = EitherError<A::Error, B::Error>;
+    type Error = Either<A::Error, B::Error>;
 
     fn poll_ready(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
         match self.project() {
-            EitherOutputProj::First(a) => Sink::poll_ready(a, cx).map_err(EitherError::A),
-            EitherOutputProj::Second(b) => Sink::poll_ready(b, cx).map_err(EitherError::B),
+            EitherOutputProj::First(a) => Sink::poll_ready(a, cx).map_err(Either::Left),
+            EitherOutputProj::Second(b) => Sink::poll_ready(b, cx).map_err(Either::Right),
         }
     }
 
     fn start_send(self: Pin<&mut Self>, item: I) -> Result<(), Self::Error> {
         match self.project() {
-            EitherOutputProj::First(a) => Sink::start_send(a, item).map_err(EitherError::A),
-            EitherOutputProj::Second(b) => Sink::start_send(b, item).map_err(EitherError::B),
+            EitherOutputProj::First(a) => Sink::start_send(a, item).map_err(Either::Left),
+            EitherOutputProj::Second(b) => Sink::start_send(b, item).map_err(Either::Right),
         }
     }
 
     fn poll_flush(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
         match self.project() {
-            EitherOutputProj::First(a) => Sink::poll_flush(a, cx).map_err(EitherError::A),
-            EitherOutputProj::Second(b) => Sink::poll_flush(b, cx).map_err(EitherError::B),
+            EitherOutputProj::First(a) => Sink::poll_flush(a, cx).map_err(Either::Left),
+            EitherOutputProj::Second(b) => Sink::poll_flush(b, cx).map_err(Either::Right),
         }
     }
 
     fn poll_close(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
         match self.project() {
-            EitherOutputProj::First(a) => Sink::poll_close(a, cx).map_err(EitherError::A),
-            EitherOutputProj::Second(b) => Sink::poll_close(b, cx).map_err(EitherError::B),
+            EitherOutputProj::First(a) => Sink::poll_close(a, cx).map_err(Either::Left),
+            EitherOutputProj::Second(b) => Sink::poll_close(b, cx).map_err(Either::Right),
         }
     }
 }
@@ -203,7 +172,7 @@ where
     B: StreamMuxer,
 {
     type Substream = EitherOutput<A::Substream, B::Substream>;
-    type Error = EitherError<A::Error, B::Error>;
+    type Error = Either<A::Error, B::Error>;
 
     fn poll_inbound(
         self: Pin<&mut Self>,
@@ -213,11 +182,11 @@ where
             EitherOutputProj::First(inner) => inner
                 .poll_inbound(cx)
                 .map_ok(EitherOutput::First)
-                .map_err(EitherError::A),
+                .map_err(Either::Left),
             EitherOutputProj::Second(inner) => inner
                 .poll_inbound(cx)
                 .map_ok(EitherOutput::Second)
-                .map_err(EitherError::B),
+                .map_err(Either::Right),
         }
     }
 
@@ -229,18 +198,18 @@ where
             EitherOutputProj::First(inner) => inner
                 .poll_outbound(cx)
                 .map_ok(EitherOutput::First)
-                .map_err(EitherError::A),
+                .map_err(Either::Left),
             EitherOutputProj::Second(inner) => inner
                 .poll_outbound(cx)
                 .map_ok(EitherOutput::Second)
-                .map_err(EitherError::B),
+                .map_err(Either::Right),
         }
     }
 
     fn poll_close(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
         match self.project() {
-            EitherOutputProj::First(inner) => inner.poll_close(cx).map_err(EitherError::A),
-            EitherOutputProj::Second(inner) => inner.poll_close(cx).map_err(EitherError::B),
+            EitherOutputProj::First(inner) => inner.poll_close(cx).map_err(Either::Left),
+            EitherOutputProj::Second(inner) => inner.poll_close(cx).map_err(Either::Right),
         }
     }
 
@@ -249,8 +218,8 @@ where
         cx: &mut Context<'_>,
     ) -> Poll<Result<StreamMuxerEvent, Self::Error>> {
         match self.project() {
-            EitherOutputProj::First(inner) => inner.poll(cx).map_err(EitherError::A),
-            EitherOutputProj::Second(inner) => inner.poll(cx).map_err(EitherError::B),
+            EitherOutputProj::First(inner) => inner.poll(cx).map_err(Either::Left),
+            EitherOutputProj::Second(inner) => inner.poll(cx).map_err(Either::Right),
         }
     }
 }
@@ -269,16 +238,16 @@ where
     AFuture: TryFuture<Ok = AInner>,
     BFuture: TryFuture<Ok = BInner>,
 {
-    type Output = Result<EitherOutput<AInner, BInner>, EitherError<AFuture::Error, BFuture::Error>>;
+    type Output = Result<EitherOutput<AInner, BInner>, Either<AFuture::Error, BFuture::Error>>;
 
     fn poll(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
         match self.project() {
             EitherFutureProj::First(a) => TryFuture::try_poll(a, cx)
                 .map_ok(EitherOutput::First)
-                .map_err(EitherError::A),
+                .map_err(Either::Left),
             EitherFutureProj::Second(a) => TryFuture::try_poll(a, cx)
                 .map_ok(EitherOutput::Second)
-                .map_err(EitherError::B),
+                .map_err(Either::Right),
         }
     }
 }
@@ -296,16 +265,16 @@ where
     AFut: TryFuture<Ok = AItem, Error = AError>,
     BFut: TryFuture<Ok = BItem, Error = BError>,
 {
-    type Output = Result<EitherOutput<AItem, BItem>, EitherError<AError, BError>>;
+    type Output = Result<EitherOutput<AItem, BItem>, Either<AError, BError>>;
 
     fn poll(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
         match self.project() {
             EitherFuture2Proj::A(a) => TryFuture::try_poll(a, cx)
                 .map_ok(EitherOutput::First)
-                .map_err(EitherError::A),
+                .map_err(Either::Left),
             EitherFuture2Proj::B(a) => TryFuture::try_poll(a, cx)
                 .map_ok(EitherOutput::Second)
-                .map_err(EitherError::B),
+                .map_err(Either::Right),
         }
     }
 }
@@ -338,7 +307,7 @@ where
     A: Transport,
 {
     type Output = EitherOutput<A::Output, B::Output>;
-    type Error = EitherError<A::Error, B::Error>;
+    type Error = Either<A::Error, B::Error>;
     type ListenerUpgrade = EitherFuture<A::ListenerUpgrade, B::ListenerUpgrade>;
     type Dial = EitherFuture<A::Dial, B::Dial>;
 
@@ -349,18 +318,16 @@ where
         match self.project() {
             EitherTransportProj::Left(a) => match a.poll(cx) {
                 Poll::Pending => Poll::Pending,
-                Poll::Ready(event) => Poll::Ready(
-                    event
-                        .map_upgrade(EitherFuture::First)
-                        .map_err(EitherError::A),
-                ),
+                Poll::Ready(event) => {
+                    Poll::Ready(event.map_upgrade(EitherFuture::First).map_err(Either::Left))
+                }
             },
             EitherTransportProj::Right(b) => match b.poll(cx) {
                 Poll::Pending => Poll::Pending,
                 Poll::Ready(event) => Poll::Ready(
                     event
                         .map_upgrade(EitherFuture::Second)
-                        .map_err(EitherError::B),
+                        .map_err(Either::Right),
                 ),
             },
         }
@@ -378,11 +345,11 @@ where
         match self {
             EitherTransport::Left(a) => a.listen_on(addr).map_err(|e| match e {
                 MultiaddrNotSupported(addr) => MultiaddrNotSupported(addr),
-                Other(err) => Other(EitherError::A(err)),
+                Other(err) => Other(Either::Left(err)),
             }),
             EitherTransport::Right(b) => b.listen_on(addr).map_err(|e| match e {
                 MultiaddrNotSupported(addr) => MultiaddrNotSupported(addr),
-                Other(err) => Other(EitherError::B(err)),
+                Other(err) => Other(Either::Right(err)),
             }),
         }
     }
@@ -393,12 +360,12 @@ where
             EitherTransport::Left(a) => match a.dial(addr) {
                 Ok(connec) => Ok(EitherFuture::First(connec)),
                 Err(MultiaddrNotSupported(addr)) => Err(MultiaddrNotSupported(addr)),
-                Err(Other(err)) => Err(Other(EitherError::A(err))),
+                Err(Other(err)) => Err(Other(Either::Left(err))),
             },
             EitherTransport::Right(b) => match b.dial(addr) {
                 Ok(connec) => Ok(EitherFuture::Second(connec)),
                 Err(MultiaddrNotSupported(addr)) => Err(MultiaddrNotSupported(addr)),
-                Err(Other(err)) => Err(Other(EitherError::B(err))),
+                Err(Other(err)) => Err(Other(Either::Right(err))),
             },
         }
     }
@@ -415,12 +382,12 @@ where
             EitherTransport::Left(a) => match a.dial_as_listener(addr) {
                 Ok(connec) => Ok(EitherFuture::First(connec)),
                 Err(MultiaddrNotSupported(addr)) => Err(MultiaddrNotSupported(addr)),
-                Err(Other(err)) => Err(Other(EitherError::A(err))),
+                Err(Other(err)) => Err(Other(Either::Left(err))),
             },
             EitherTransport::Right(b) => match b.dial_as_listener(addr) {
                 Ok(connec) => Ok(EitherFuture::Second(connec)),
                 Err(MultiaddrNotSupported(addr)) => Err(MultiaddrNotSupported(addr)),
-                Err(Other(err)) => Err(Other(EitherError::B(err))),
+                Err(Other(err)) => Err(Other(Either::Right(err))),
             },
         }
     }
diff --git a/core/src/transport/and_then.rs b/core/src/transport/and_then.rs
index 561a2f281ff..fb5280568ea 100644
--- a/core/src/transport/and_then.rs
+++ b/core/src/transport/and_then.rs
@@ -20,10 +20,10 @@
 
 use crate::{
     connection::{ConnectedPoint, Endpoint},
-    either::EitherError,
     transport::{ListenerId, Transport, TransportError, TransportEvent},
 };
-use futures::{future::Either, prelude::*};
+use either::Either;
+use futures::prelude::*;
 use multiaddr::Multiaddr;
 use std::{error, marker::PhantomPinned, pin::Pin, task::Context, task::Poll};
 
@@ -50,14 +50,14 @@ where
     F::Error: error::Error,
 {
     type Output = O;
-    type Error = EitherError<T::Error, F::Error>;
+    type Error = Either<T::Error, F::Error>;
     type ListenerUpgrade = AndThenFuture<T::ListenerUpgrade, C, F>;
     type Dial = AndThenFuture<T::Dial, C, F>;
 
     fn listen_on(&mut self, addr: Multiaddr) -> Result<ListenerId, TransportError<Self::Error>> {
         self.transport
             .listen_on(addr)
-            .map_err(|err| err.map(EitherError::A))
+            .map_err(|err| err.map(Either::Left))
     }
 
     fn remove_listener(&mut self, id: ListenerId) -> bool {
@@ -68,7 +68,7 @@ where
         let dialed_fut = self
             .transport
             .dial(addr.clone())
-            .map_err(|err| err.map(EitherError::A))?;
+            .map_err(|err| err.map(Either::Left))?;
         let future = AndThenFuture {
             inner: Either::Left(Box::pin(dialed_fut)),
             args: Some((
@@ -90,7 +90,7 @@ where
         let dialed_fut = self
             .transport
             .dial_as_listener(addr.clone())
-            .map_err(|err| err.map(EitherError::A))?;
+            .map_err(|err| err.map(Either::Left))?;
         let future = AndThenFuture {
             inner: Either::Left(Box::pin(dialed_fut)),
             args: Some((
@@ -139,7 +139,7 @@ where
             Poll::Ready(other) => {
                 let mapped = other
                     .map_upgrade(|_upgrade| unreachable!("case already matched"))
-                    .map_err(EitherError::A);
+                    .map_err(Either::Left);
                 Poll::Ready(mapped)
             }
             Poll::Pending => Poll::Pending,
@@ -163,7 +163,7 @@ where
     TMap: FnOnce(TFut::Ok, ConnectedPoint) -> TMapOut,
     TMapOut: TryFuture,
 {
-    type Output = Result<TMapOut::Ok, EitherError<TFut::Error, TMapOut::Error>>;
+    type Output = Result<TMapOut::Ok, Either<TFut::Error, TMapOut::Error>>;
 
     fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
         loop {
@@ -171,7 +171,7 @@ where
                 Either::Left(future) => {
                     let item = match TryFuture::try_poll(future.as_mut(), cx) {
                         Poll::Ready(Ok(v)) => v,
-                        Poll::Ready(Err(err)) => return Poll::Ready(Err(EitherError::A(err))),
+                        Poll::Ready(Err(err)) => return Poll::Ready(Err(Either::Left(err))),
                         Poll::Pending => return Poll::Pending,
                     };
                     let (f, a) = self
@@ -183,7 +183,7 @@ where
                 Either::Right(future) => {
                     return match TryFuture::try_poll(future.as_mut(), cx) {
                         Poll::Ready(Ok(v)) => Poll::Ready(Ok(v)),
-                        Poll::Ready(Err(err)) => return Poll::Ready(Err(EitherError::B(err))),
+                        Poll::Ready(Err(err)) => return Poll::Ready(Err(Either::Right(err))),
                         Poll::Pending => Poll::Pending,
                     }
                 }
diff --git a/core/src/transport/choice.rs b/core/src/transport/choice.rs
index 17528c1d4a8..2405f013039 100644
--- a/core/src/transport/choice.rs
+++ b/core/src/transport/choice.rs
@@ -18,8 +18,9 @@
 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 // DEALINGS IN THE SOFTWARE.
 
-use crate::either::{EitherError, EitherFuture, EitherOutput};
+use crate::either::{EitherFuture, EitherOutput};
 use crate::transport::{ListenerId, Transport, TransportError, TransportEvent};
+use either::Either;
 use multiaddr::Multiaddr;
 use std::{pin::Pin, task::Context, task::Poll};
 
@@ -40,19 +41,19 @@ where
     A: Transport,
 {
     type Output = EitherOutput<A::Output, B::Output>;
-    type Error = EitherError<A::Error, B::Error>;
+    type Error = Either<A::Error, B::Error>;
     type ListenerUpgrade = EitherFuture<A::ListenerUpgrade, B::ListenerUpgrade>;
     type Dial = EitherFuture<A::Dial, B::Dial>;
 
     fn listen_on(&mut self, addr: Multiaddr) -> Result<ListenerId, TransportError<Self::Error>> {
         let addr = match self.0.listen_on(addr) {
             Err(TransportError::MultiaddrNotSupported(addr)) => addr,
-            res => return res.map_err(|err| err.map(EitherError::A)),
+            res => return res.map_err(|err| err.map(Either::Left)),
         };
 
         let addr = match self.1.listen_on(addr) {
             Err(TransportError::MultiaddrNotSupported(addr)) => addr,
-            res => return res.map_err(|err| err.map(EitherError::B)),
+            res => return res.map_err(|err| err.map(Either::Right)),
         };
 
         Err(TransportError::MultiaddrNotSupported(addr))
@@ -67,7 +68,7 @@ where
             Ok(connec) => return Ok(EitherFuture::First(connec)),
             Err(TransportError::MultiaddrNotSupported(addr)) => addr,
             Err(TransportError::Other(err)) => {
-                return Err(TransportError::Other(EitherError::A(err)))
+                return Err(TransportError::Other(Either::Left(err)))
             }
         };
 
@@ -75,7 +76,7 @@ where
             Ok(connec) => return Ok(EitherFuture::Second(connec)),
             Err(TransportError::MultiaddrNotSupported(addr)) => addr,
             Err(TransportError::Other(err)) => {
-                return Err(TransportError::Other(EitherError::B(err)))
+                return Err(TransportError::Other(Either::Right(err)))
             }
         };
 
@@ -90,7 +91,7 @@ where
             Ok(connec) => return Ok(EitherFuture::First(connec)),
             Err(TransportError::MultiaddrNotSupported(addr)) => addr,
             Err(TransportError::Other(err)) => {
-                return Err(TransportError::Other(EitherError::A(err)))
+                return Err(TransportError::Other(Either::Left(err)))
             }
         };
 
@@ -98,7 +99,7 @@ where
             Ok(connec) => return Ok(EitherFuture::Second(connec)),
             Err(TransportError::MultiaddrNotSupported(addr)) => addr,
             Err(TransportError::Other(err)) => {
-                return Err(TransportError::Other(EitherError::B(err)))
+                return Err(TransportError::Other(Either::Right(err)))
             }
         };
 
@@ -120,13 +121,13 @@ where
         let this = self.project();
         match this.0.poll(cx) {
             Poll::Ready(ev) => {
-                return Poll::Ready(ev.map_upgrade(EitherFuture::First).map_err(EitherError::A))
+                return Poll::Ready(ev.map_upgrade(EitherFuture::First).map_err(Either::Left))
             }
             Poll::Pending => {}
         }
         match this.1.poll(cx) {
             Poll::Ready(ev) => {
-                return Poll::Ready(ev.map_upgrade(EitherFuture::Second).map_err(EitherError::B))
+                return Poll::Ready(ev.map_upgrade(EitherFuture::Second).map_err(Either::Right))
             }
             Poll::Pending => {}
         }
diff --git a/core/src/upgrade/either.rs b/core/src/upgrade/either.rs
index 8b5c7f71422..99a2f557e5f 100644
--- a/core/src/upgrade/either.rs
+++ b/core/src/upgrade/either.rs
@@ -19,9 +19,10 @@
 // DEALINGS IN THE SOFTWARE.
 
 use crate::{
-    either::{EitherError, EitherFuture2, EitherName, EitherOutput},
+    either::{EitherFuture2, EitherName, EitherOutput},
     upgrade::{InboundUpgrade, OutboundUpgrade, UpgradeInfo},
 };
+use either::Either;
 
 /// A type to represent two possible upgrade types (inbound or outbound).
 #[derive(Debug, Clone)]
@@ -55,7 +56,7 @@ where
     B: InboundUpgrade<C, Output = TB, Error = EB>,
 {
     type Output = EitherOutput<TA, TB>;
-    type Error = EitherError<EA, EB>;
+    type Error = Either<EA, EB>;
     type Future = EitherFuture2<A::Future, B::Future>;
 
     fn upgrade_inbound(self, sock: C, info: Self::Info) -> Self::Future {
@@ -77,7 +78,7 @@ where
     B: OutboundUpgrade<C, Output = TB, Error = EB>,
 {
     type Output = EitherOutput<TA, TB>;
-    type Error = EitherError<EA, EB>;
+    type Error = Either<EA, EB>;
     type Future = EitherFuture2<A::Future, B::Future>;
 
     fn upgrade_outbound(self, sock: C, info: Self::Info) -> Self::Future {
diff --git a/core/src/upgrade/select.rs b/core/src/upgrade/select.rs
index d1a8cabca2f..fed93bc0430 100644
--- a/core/src/upgrade/select.rs
+++ b/core/src/upgrade/select.rs
@@ -19,9 +19,10 @@
 // DEALINGS IN THE SOFTWARE.
 
 use crate::{
-    either::{EitherError, EitherFuture2, EitherName, EitherOutput},
+    either::{EitherFuture2, EitherName, EitherOutput},
     upgrade::{InboundUpgrade, OutboundUpgrade, UpgradeInfo},
 };
+use either::Either;
 
 /// Upgrade that combines two upgrades into one. Supports all the protocols supported by either
 /// sub-upgrade.
@@ -64,7 +65,7 @@ where
     B: InboundUpgrade<C, Output = TB, Error = EB>,
 {
     type Output = EitherOutput<TA, TB>;
-    type Error = EitherError<EA, EB>;
+    type Error = Either<EA, EB>;
     type Future = EitherFuture2<A::Future, B::Future>;
 
     fn upgrade_inbound(self, sock: C, info: Self::Info) -> Self::Future {
@@ -81,7 +82,7 @@ where
     B: OutboundUpgrade<C, Output = TB, Error = EB>,
 {
     type Output = EitherOutput<TA, TB>;
-    type Error = EitherError<EA, EB>;
+    type Error = Either<EA, EB>;
     type Future = EitherFuture2<A::Future, B::Future>;
 
     fn upgrade_outbound(self, sock: C, info: Self::Info) -> Self::Future {
diff --git a/examples/file-sharing.rs b/examples/file-sharing.rs
index b38f456972b..6cae1f492a5 100644
--- a/examples/file-sharing.rs
+++ b/examples/file-sharing.rs
@@ -207,8 +207,8 @@ enum CliArgument {
 mod network {
     use super::*;
     use async_trait::async_trait;
+    use either::Either;
     use futures::channel::{mpsc, oneshot};
-    use libp2p::core::either::EitherError;
     use libp2p::core::upgrade::{read_length_prefixed, write_length_prefixed, ProtocolName};
     use libp2p::identity;
     use libp2p::identity::ed25519;
@@ -405,7 +405,7 @@ mod network {
             &mut self,
             event: SwarmEvent<
                 ComposedEvent,
-                EitherError<ConnectionHandlerUpgrErr<io::Error>, io::Error>,
+                Either<ConnectionHandlerUpgrErr<io::Error>, io::Error>,
             >,
         ) {
             match event {
diff --git a/protocols/dcutr/src/handler/relayed.rs b/protocols/dcutr/src/handler/relayed.rs
index 301f2ee3d82..7e8270629ed 100644
--- a/protocols/dcutr/src/handler/relayed.rs
+++ b/protocols/dcutr/src/handler/relayed.rs
@@ -21,9 +21,10 @@
 //! [`ConnectionHandler`] handling relayed connection potentially upgraded to a direct connection.
 
 use crate::protocol;
+use either::Either;
 use futures::future::{BoxFuture, FutureExt};
 use instant::Instant;
-use libp2p_core::either::{EitherError, EitherOutput};
+use libp2p_core::either::EitherOutput;
 use libp2p_core::multiaddr::Multiaddr;
 use libp2p_core::upgrade::{self, DeniedUpgrade, NegotiationError, UpgradeError};
 use libp2p_core::ConnectedPoint;
@@ -134,7 +135,7 @@ pub struct Handler {
     /// A pending fatal error that results in the connection being closed.
     pending_error: Option<
         ConnectionHandlerUpgrErr<
-            EitherError<protocol::inbound::UpgradeError, protocol::outbound::UpgradeError>,
+            Either<protocol::inbound::UpgradeError, protocol::outbound::UpgradeError>,
         >,
     >,
     /// Queue of events to return when polled.
@@ -252,8 +253,8 @@ impl Handler {
                 // the remote peer and results in closing the connection.
                 self.pending_error = Some(error.map_upgrade_err(|e| {
                     e.map_err(|e| match e {
-                        EitherError::A(e) => EitherError::A(e),
-                        EitherError::B(v) => void::unreachable(v),
+                        Either::Left(e) => Either::Left(e),
+                        Either::Right(v) => void::unreachable(v),
                     })
                 }));
             }
@@ -292,7 +293,7 @@ impl Handler {
             _ => {
                 // Anything else is considered a fatal error or misbehaviour of
                 // the remote peer and results in closing the connection.
-                self.pending_error = Some(error.map_upgrade_err(|e| e.map_err(EitherError::B)));
+                self.pending_error = Some(error.map_upgrade_err(|e| e.map_err(Either::Right)));
             }
         }
     }
@@ -302,7 +303,7 @@ impl ConnectionHandler for Handler {
     type InEvent = Command;
     type OutEvent = Event;
     type Error = ConnectionHandlerUpgrErr<
-        EitherError<protocol::inbound::UpgradeError, protocol::outbound::UpgradeError>,
+        Either<protocol::inbound::UpgradeError, protocol::outbound::UpgradeError>,
     >;
     type InboundProtocol = upgrade::EitherUpgrade<protocol::inbound::Upgrade, DeniedUpgrade>;
     type OutboundProtocol = protocol::outbound::Upgrade;
@@ -393,7 +394,7 @@ impl ConnectionHandler for Handler {
                 }
                 Err(e) => {
                     return Poll::Ready(ConnectionHandlerEvent::Close(
-                        ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(EitherError::A(e))),
+                        ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(Either::Left(e))),
                     ))
                 }
             }
diff --git a/protocols/identify/Cargo.toml b/protocols/identify/Cargo.toml
index bc3316d9bb0..3e844a2c8d0 100644
--- a/protocols/identify/Cargo.toml
+++ b/protocols/identify/Cargo.toml
@@ -23,6 +23,7 @@ prost = "0.11"
 smallvec = "1.6.1"
 thiserror = "1.0"
 void = "1.0"
+either = "1.8.0"
 
 [dev-dependencies]
 async-std = { version = "1.6.2", features = ["attributes"] }
diff --git a/protocols/identify/src/handler.rs b/protocols/identify/src/handler.rs
index 21063acc661..0dce0e49940 100644
--- a/protocols/identify/src/handler.rs
+++ b/protocols/identify/src/handler.rs
@@ -21,11 +21,12 @@
 use crate::protocol::{
     self, Identify, InboundPush, Info, OutboundPush, Protocol, Push, UpgradeError,
 };
+use either::Either;
 use futures::future::BoxFuture;
 use futures::prelude::*;
 use futures::stream::FuturesUnordered;
 use futures_timer::Delay;
-use libp2p_core::either::{EitherError, EitherOutput};
+use libp2p_core::either::EitherOutput;
 use libp2p_core::upgrade::{EitherUpgrade, SelectUpgrade};
 use libp2p_core::{ConnectedPoint, Multiaddr, PeerId, PublicKey};
 use libp2p_swarm::handler::{
@@ -259,8 +260,8 @@ impl Handler {
 
         let err = err.map_upgrade_err(|e| match e {
             UpgradeError::Select(e) => UpgradeError::Select(e),
-            UpgradeError::Apply(EitherError::A(ioe)) => UpgradeError::Apply(ioe),
-            UpgradeError::Apply(EitherError::B(ioe)) => UpgradeError::Apply(ioe),
+            UpgradeError::Apply(Either::Left(ioe)) => UpgradeError::Apply(ioe),
+            UpgradeError::Apply(Either::Right(ioe)) => UpgradeError::Apply(ioe),
         });
         self.events
             .push(ConnectionHandlerEvent::Custom(Event::IdentificationError(
diff --git a/protocols/relay/src/behaviour/handler.rs b/protocols/relay/src/behaviour/handler.rs
index 120e980c001..1aaa47b6345 100644
--- a/protocols/relay/src/behaviour/handler.rs
+++ b/protocols/relay/src/behaviour/handler.rs
@@ -31,7 +31,6 @@ use futures::stream::{FuturesUnordered, StreamExt};
 use futures_timer::Delay;
 use instant::Instant;
 use libp2p_core::connection::ConnectionId;
-use libp2p_core::either::EitherError;
 use libp2p_core::{upgrade, ConnectedPoint, Multiaddr, PeerId};
 use libp2p_swarm::handler::{
     ConnectionEvent, DialUpgradeError, FullyNegotiatedInbound, FullyNegotiatedOutbound,
@@ -397,7 +396,7 @@ pub struct Handler {
     /// A pending fatal error that results in the connection being closed.
     pending_error: Option<
         ConnectionHandlerUpgrErr<
-            EitherError<inbound_hop::FatalUpgradeError, outbound_stop::FatalUpgradeError>,
+            Either<inbound_hop::FatalUpgradeError, outbound_stop::FatalUpgradeError>,
         >,
     >,
 
@@ -521,7 +520,7 @@ impl Handler {
                 inbound_hop::UpgradeError::Fatal(error),
             )) => {
                 self.pending_error = Some(ConnectionHandlerUpgrErr::Upgrade(
-                    upgrade::UpgradeError::Apply(EitherError::A(error)),
+                    upgrade::UpgradeError::Apply(Either::Left(error)),
                 ));
                 return;
             }
@@ -572,7 +571,7 @@ impl Handler {
             ConnectionHandlerUpgrErr::Upgrade(upgrade::UpgradeError::Apply(error)) => match error {
                 outbound_stop::UpgradeError::Fatal(error) => {
                     self.pending_error = Some(ConnectionHandlerUpgrErr::Upgrade(
-                        upgrade::UpgradeError::Apply(EitherError::B(error)),
+                        upgrade::UpgradeError::Apply(Either::Right(error)),
                     ));
                     return;
                 }
@@ -624,7 +623,7 @@ impl ConnectionHandler for Handler {
     type InEvent = In;
     type OutEvent = Event;
     type Error = ConnectionHandlerUpgrErr<
-        EitherError<inbound_hop::FatalUpgradeError, outbound_stop::FatalUpgradeError>,
+        Either<inbound_hop::FatalUpgradeError, outbound_stop::FatalUpgradeError>,
     >;
     type InboundProtocol = inbound_hop::Upgrade;
     type OutboundProtocol = outbound_stop::Upgrade;
diff --git a/protocols/relay/src/priv_client/handler.rs b/protocols/relay/src/priv_client/handler.rs
index c9f7c18adbb..d64732766b1 100644
--- a/protocols/relay/src/priv_client/handler.rs
+++ b/protocols/relay/src/priv_client/handler.rs
@@ -28,7 +28,6 @@ use futures::sink::SinkExt;
 use futures::stream::{FuturesUnordered, StreamExt};
 use futures_timer::Delay;
 use instant::Instant;
-use libp2p_core::either::EitherError;
 use libp2p_core::multiaddr::Protocol;
 use libp2p_core::{upgrade, ConnectedPoint, Multiaddr, PeerId};
 use libp2p_swarm::handler::{
@@ -174,7 +173,7 @@ pub struct Handler {
     /// A pending fatal error that results in the connection being closed.
     pending_error: Option<
         ConnectionHandlerUpgrErr<
-            EitherError<inbound_stop::FatalUpgradeError, outbound_hop::FatalUpgradeError>,
+            Either<inbound_stop::FatalUpgradeError, outbound_hop::FatalUpgradeError>,
         >,
     >,
     /// Until when to keep the connection alive.
@@ -366,7 +365,7 @@ impl Handler {
                 inbound_stop::UpgradeError::Fatal(error),
             )) => {
                 self.pending_error = Some(ConnectionHandlerUpgrErr::Upgrade(
-                    upgrade::UpgradeError::Apply(EitherError::A(error)),
+                    upgrade::UpgradeError::Apply(Either::Left(error)),
                 ));
                 return;
             }
@@ -413,7 +412,7 @@ impl Handler {
                         match error {
                             outbound_hop::UpgradeError::Fatal(error) => {
                                 self.pending_error = Some(ConnectionHandlerUpgrErr::Upgrade(
-                                    upgrade::UpgradeError::Apply(EitherError::B(error)),
+                                    upgrade::UpgradeError::Apply(Either::Right(error)),
                                 ));
                                 return;
                             }
@@ -476,7 +475,7 @@ impl Handler {
                         match error {
                             outbound_hop::UpgradeError::Fatal(error) => {
                                 self.pending_error = Some(ConnectionHandlerUpgrErr::Upgrade(
-                                    upgrade::UpgradeError::Apply(EitherError::B(error)),
+                                    upgrade::UpgradeError::Apply(Either::Right(error)),
                                 ));
                                 return;
                             }
@@ -510,7 +509,7 @@ impl ConnectionHandler for Handler {
     type InEvent = In;
     type OutEvent = Event;
     type Error = ConnectionHandlerUpgrErr<
-        EitherError<inbound_stop::FatalUpgradeError, outbound_hop::FatalUpgradeError>,
+        Either<inbound_stop::FatalUpgradeError, outbound_hop::FatalUpgradeError>,
     >;
     type InboundProtocol = inbound_stop::Upgrade;
     type OutboundProtocol = outbound_hop::Upgrade;
diff --git a/swarm/src/behaviour/toggle.rs b/swarm/src/behaviour/toggle.rs
index ae198dc2bd3..1606e5e53a3 100644
--- a/swarm/src/behaviour/toggle.rs
+++ b/swarm/src/behaviour/toggle.rs
@@ -28,7 +28,7 @@ use crate::upgrade::SendWrapper;
 use crate::{NetworkBehaviour, NetworkBehaviourAction, PollParameters};
 use either::Either;
 use libp2p_core::{
-    either::{EitherError, EitherOutput},
+    either::EitherOutput,
     upgrade::{DeniedUpgrade, EitherUpgrade},
     ConnectedPoint, Multiaddr, PeerId,
 };
@@ -215,8 +215,8 @@ where
             ConnectionHandlerUpgrErr::Timer => ConnectionHandlerUpgrErr::Timer,
             ConnectionHandlerUpgrErr::Upgrade(err) => {
                 ConnectionHandlerUpgrErr::Upgrade(err.map_err(|err| match err {
-                    EitherError::A(e) => e,
-                    EitherError::B(v) => void::unreachable(v),
+                    Either::Left(e) => e,
+                    Either::Right(v) => void::unreachable(v),
                 }))
             }
         };
diff --git a/swarm/src/handler/either.rs b/swarm/src/handler/either.rs
index 4be677a55f6..f03afb20499 100644
--- a/swarm/src/handler/either.rs
+++ b/swarm/src/handler/either.rs
@@ -25,7 +25,7 @@ use crate::handler::{
 };
 use crate::upgrade::SendWrapper;
 use either::Either;
-use libp2p_core::either::{EitherError, EitherOutput};
+use libp2p_core::either::EitherOutput;
 use libp2p_core::upgrade::{EitherUpgrade, UpgradeError};
 use libp2p_core::{ConnectedPoint, PeerId};
 use std::task::{Context, Poll};
@@ -145,14 +145,14 @@ where
     fn transpose(self) -> Either<DialUpgradeError<LOOI, LOP>, DialUpgradeError<ROOI, ROP>> {
         match self {
             DialUpgradeError {
-                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(EitherError::A(error))),
+                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(Either::Left(error))),
                 info: Either::Left(info),
             } => Either::Left(DialUpgradeError {
                 error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(error)),
                 info,
             }),
             DialUpgradeError {
-                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(EitherError::B(error))),
+                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(Either::Right(error))),
                 info: Either::Right(info),
             } => Either::Right(DialUpgradeError {
                 error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(error)),
@@ -214,14 +214,14 @@ where
     fn transpose(self) -> Either<ListenUpgradeError<LIOI, LIP>, ListenUpgradeError<RIOI, RIP>> {
         match self {
             ListenUpgradeError {
-                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(EitherError::A(error))),
+                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(Either::Left(error))),
                 info: Either::Left(info),
             } => Either::Left(ListenUpgradeError {
                 error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(error)),
                 info,
             }),
             ListenUpgradeError {
-                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(EitherError::B(error))),
+                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(Either::Right(error))),
                 info: Either::Right(info),
             } => Either::Right(ListenUpgradeError {
                 error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(error)),
diff --git a/swarm/src/handler/select.rs b/swarm/src/handler/select.rs
index c979d91c71e..8d052d637d7 100644
--- a/swarm/src/handler/select.rs
+++ b/swarm/src/handler/select.rs
@@ -28,7 +28,7 @@ use crate::upgrade::SendWrapper;
 
 use either::Either;
 use libp2p_core::{
-    either::{EitherError, EitherOutput},
+    either::EitherOutput,
     upgrade::{EitherUpgrade, NegotiationError, ProtocolError, SelectUpgrade, UpgradeError},
     ConnectedPoint, PeerId,
 };
@@ -186,7 +186,7 @@ where
             }),
             DialUpgradeError {
                 info: EitherOutput::First(info),
-                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(EitherError::A(err))),
+                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(Either::Left(err))),
             } => Either::Left(DialUpgradeError {
                 info,
                 error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(err)),
@@ -214,7 +214,7 @@ where
             }),
             DialUpgradeError {
                 info: EitherOutput::Second(info),
-                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(EitherError::B(err))),
+                error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(Either::Right(err))),
             } => Either::Right(DialUpgradeError {
                 info,
                 error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(err)),
@@ -318,14 +318,14 @@ where
                         error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Select(e2)),
                     }));
             }
-            ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(EitherError::A(e))) => {
+            ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(Either::Left(e))) => {
                 self.proto1
                     .on_connection_event(ConnectionEvent::ListenUpgradeError(ListenUpgradeError {
                         info: i1,
                         error: ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(e)),
                     }));
             }
-            ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(EitherError::B(e))) => {
+            ConnectionHandlerUpgrErr::Upgrade(UpgradeError::Apply(Either::Right(e))) => {
                 self.proto2
                     .on_connection_event(ConnectionEvent::ListenUpgradeError(ListenUpgradeError {
                         info: i2,
@@ -343,7 +343,7 @@ where
 {
     type InEvent = EitherOutput<TProto1::InEvent, TProto2::InEvent>;
     type OutEvent = EitherOutput<TProto1::OutEvent, TProto2::OutEvent>;
-    type Error = EitherError<TProto1::Error, TProto2::Error>;
+    type Error = Either<TProto1::Error, TProto2::Error>;
     type InboundProtocol = SelectUpgrade<
         SendWrapper<<TProto1 as ConnectionHandler>::InboundProtocol>,
         SendWrapper<<TProto2 as ConnectionHandler>::InboundProtocol>,
@@ -395,7 +395,7 @@ where
                 return Poll::Ready(ConnectionHandlerEvent::Custom(EitherOutput::First(event)));
             }
             Poll::Ready(ConnectionHandlerEvent::Close(event)) => {
-                return Poll::Ready(ConnectionHandlerEvent::Close(EitherError::A(event)));
+                return Poll::Ready(ConnectionHandlerEvent::Close(Either::Left(event)));
             }
             Poll::Ready(ConnectionHandlerEvent::OutboundSubstreamRequest { protocol }) => {
                 return Poll::Ready(ConnectionHandlerEvent::OutboundSubstreamRequest {
@@ -412,7 +412,7 @@ where
                 return Poll::Ready(ConnectionHandlerEvent::Custom(EitherOutput::Second(event)));
             }
             Poll::Ready(ConnectionHandlerEvent::Close(event)) => {
-                return Poll::Ready(ConnectionHandlerEvent::Close(EitherError::B(event)));
+                return Poll::Ready(ConnectionHandlerEvent::Close(Either::Right(event)));
             }
             Poll::Ready(ConnectionHandlerEvent::OutboundSubstreamRequest { protocol }) => {
                 return Poll::Ready(ConnectionHandlerEvent::OutboundSubstreamRequest {
diff --git a/swarm/src/lib.rs b/swarm/src/lib.rs
index cf0b4c3b08a..47fc410a356 100644
--- a/swarm/src/lib.rs
+++ b/swarm/src/lib.rs
@@ -1750,12 +1750,11 @@ fn p2p_addr(peer: Option<PeerId>, addr: Multiaddr) -> Result<Multiaddr, Multiadd
 mod tests {
     use super::*;
     use crate::test::{CallTraceBehaviour, MockBehaviour};
+    use either::Either;
     use futures::executor::block_on;
     use futures::executor::ThreadPool;
     use futures::future::poll_fn;
-    use futures::future::Either;
     use futures::{executor, future, ready};
-    use libp2p_core::either::EitherError;
     use libp2p_core::multiaddr::multiaddr;
     use libp2p_core::transport::memory::MemoryTransportError;
     use libp2p_core::transport::TransportEvent;
@@ -2225,13 +2224,13 @@ mod tests {
                         match futures::future::select(transport.select_next_some(), swarm.next())
                             .await
                         {
-                            Either::Left((TransportEvent::Incoming { .. }, _)) => {
+                            future::Either::Left((TransportEvent::Incoming { .. }, _)) => {
                                 break;
                             }
-                            Either::Left(_) => {
+                            future::Either::Left(_) => {
                                 panic!("Unexpected transport event.")
                             }
-                            Either::Right((e, _)) => {
+                            future::Either::Right((e, _)) => {
                                 panic!("Expect swarm to not emit any event {e:?}")
                             }
                         }
@@ -2633,7 +2632,7 @@ mod tests {
             "/ip4/127.0.0.1/tcp/80".parse().unwrap(),
             TransportError::Other(io::Error::new(
                 io::ErrorKind::Other,
-                EitherError::<_, Void>::A(EitherError::<Void, _>::B(UpgradeError::Apply(
+                Either::<_, Void>::Left(Either::<Void, _>::Right(UpgradeError::Apply(
                     MemoryTransportError::Unreachable,
                 ))),
             )),