diff --git a/multiplex.go b/multiplex.go
index fc25158..6fe3c61 100644
--- a/multiplex.go
+++ b/multiplex.go
@@ -39,7 +39,7 @@ var errTimeout = timeout{}
 
 var (
 	ResetStreamTimeout = 2 * time.Minute
-
+	MaxIncomingStreams = 1000
 	WriteCoalesceDelay = 100 * time.Microsecond
 )
 
@@ -83,22 +83,26 @@ type Multiplex struct {
 
 	nstreams chan *Stream
 
-	channels map[streamID]*Stream
-	chLock   sync.Mutex
+	maxIncoming int
+
+	channels    map[streamID]*Stream
+	numIncoming int
+	chLock      sync.Mutex
 }
 
 // NewMultiplex creates a new multiplexer session.
 func NewMultiplex(con net.Conn, initiator bool) *Multiplex {
 	mp := &Multiplex{
-		con:        con,
-		initiator:  initiator,
-		buf:        bufio.NewReader(con),
-		channels:   make(map[streamID]*Stream),
-		closed:     make(chan struct{}),
-		shutdown:   make(chan struct{}),
-		writeCh:    make(chan []byte, 16),
-		writeTimer: time.NewTimer(0),
-		nstreams:   make(chan *Stream, 16),
+		con:         con,
+		initiator:   initiator,
+		buf:         bufio.NewReader(con),
+		channels:    make(map[streamID]*Stream),
+		closed:      make(chan struct{}),
+		shutdown:    make(chan struct{}),
+		writeCh:     make(chan []byte, 16),
+		writeTimer:  time.NewTimer(0),
+		maxIncoming: MaxIncomingStreams,
+		nstreams:    make(chan *Stream, 16),
 	}
 
 	go mp.handleIncoming()
@@ -410,6 +414,15 @@ func (mp *Multiplex) handleIncoming() {
 
 			msch = mp.newStream(ch, name)
 			mp.chLock.Lock()
+			if remoteIsInitiator {
+				if mp.numIncoming >= mp.maxIncoming {
+					msch.mp.sendResetMsg(msch.id.header(resetTag), true)
+					mp.chLock.Unlock()
+					continue
+				} else {
+					mp.numIncoming++
+				}
+			}
 			mp.channels[ch] = msch
 			mp.chLock.Unlock()
 			select {
@@ -436,6 +449,9 @@ func (mp *Multiplex) handleIncoming() {
 			// unregister and throw away future data.
 			mp.chLock.Lock()
 			delete(mp.channels, ch)
+			if remoteIsInitiator {
+				mp.numIncoming--
+			}
 			mp.chLock.Unlock()
 
 			// close data channel, there will be no more data.
diff --git a/multiplex_test.go b/multiplex_test.go
index 1f27f24..aa79541 100644
--- a/multiplex_test.go
+++ b/multiplex_test.go
@@ -11,6 +11,8 @@ import (
 	"sync"
 	"testing"
 	"time"
+
+	"github.com/stretchr/testify/require"
 )
 
 func init() {
@@ -880,3 +882,48 @@ func arrComp(a, b []byte) error {
 	}
 	return nil
 }
+
+func TestMaxIncomingStreams(t *testing.T) {
+	a, b := net.Pipe()
+	client := NewMultiplex(a, true)
+	defer client.Close()
+
+	server := NewMultiplex(b, false)
+	defer server.Close()
+
+	go func() {
+		for {
+			str, err := server.Accept()
+			if err != nil {
+				return
+			}
+			_, err = str.Write([]byte("foobar"))
+			require.NoError(t, err)
+		}
+	}()
+
+	var streams []*Stream
+	for i := 0; i < MaxIncomingStreams; i++ {
+		str, err := client.NewStream(context.Background())
+		require.NoError(t, err)
+		_, err = str.Read(make([]byte, 6))
+		require.NoError(t, err)
+		streams = append(streams, str)
+	}
+	// The server now has maxIncomingStreams incoming streams.
+	// It will now reset the next stream that is opened.
+	str, err := client.NewStream(context.Background())
+	require.NoError(t, err)
+	str.SetDeadline(time.Now().Add(time.Second))
+	_, err = str.Read([]byte{0})
+	require.EqualError(t, err, "stream reset")
+
+	// Now close one of the streams.
+	// This should then allow the client to open a new stream.
+	streams[0].Close()
+	str, err = client.NewStream(context.Background())
+	require.NoError(t, err)
+	str.SetDeadline(time.Now().Add(time.Second))
+	_, err = str.Read([]byte{0})
+	require.NoError(t, err)
+}