diff --git a/h2mux/h2mux.go b/h2mux/h2mux.go
index 2b6defde..70da0447 100644
--- a/h2mux/h2mux.go
+++ b/h2mux/h2mux.go
@@ -321,24 +321,51 @@ func joinErrorsWithTimeout(errChan <-chan error, receiveCount int, timeout time.
 func (m *Muxer) Serve(ctx context.Context) error {
 	errGroup, _ := errgroup.WithContext(ctx)
 	errGroup.Go(func() error {
-		err := m.muxReader.run(m.config.Logger)
-		m.explicitShutdown.Fuse(false)
-		m.r.Close()
-		m.abort()
-		return err
+		ch := make(chan error)
+		go func() {
+			err := m.muxReader.run(m.config.Logger)
+			m.explicitShutdown.Fuse(false)
+			m.r.Close()
+			m.abort()
+			ch <- err
+		}()
+		select {
+		case err := <-ch:
+			return err
+		case <-ctx.Done():
+			return ctx.Err()
+		}
 	})
 
 	errGroup.Go(func() error {
-		err := m.muxWriter.run(m.config.Logger)
-		m.explicitShutdown.Fuse(false)
-		m.w.Close()
-		m.abort()
-		return err
+		ch := make(chan error)
+		go func() {
+			err := m.muxWriter.run(m.config.Logger)
+			m.explicitShutdown.Fuse(false)
+			m.w.Close()
+			m.abort()
+			ch <- err
+		}()
+		select {
+		case err := <-ch:
+			return err
+		case <-ctx.Done():
+			return ctx.Err()
+		}
 	})
 
 	errGroup.Go(func() error {
-		err := m.muxMetricsUpdater.run(m.config.Logger)
-		return err
+		ch := make(chan error)
+		go func() {
+			err := m.muxMetricsUpdater.run(m.config.Logger)
+			ch <- err
+		}()
+		select {
+		case err := <-ch:
+			return err
+		case <-ctx.Done():
+			return ctx.Err()
+		}
 	})
 
 	err := errGroup.Wait()