diff --git a/libp2p/network/connection/swarm_connection.py b/libp2p/network/connection/swarm_connection.py
index a4fc8be..90cb823 100644
--- a/libp2p/network/connection/swarm_connection.py
+++ b/libp2p/network/connection/swarm_connection.py
@@ -54,7 +54,7 @@ class SwarmConn(INetConn, Service):
         # before we cancel the stream handler tasks.
         await trio.sleep(0.1)
 
-        await self._notify_disconnected()
+        self._notify_disconnected()
 
     async def _handle_new_streams(self) -> None:
         while self.manager.is_running:
@@ -68,7 +68,7 @@ class SwarmConn(INetConn, Service):
         await self.close()
 
     async def _handle_muxed_stream(self, muxed_stream: IMuxedStream) -> None:
-        net_stream = await self._add_stream(muxed_stream)
+        net_stream = self._add_stream(muxed_stream)
         if self.swarm.common_stream_handler is not None:
             try:
                 await self.swarm.common_stream_handler(net_stream)
@@ -78,14 +78,14 @@ class SwarmConn(INetConn, Service):
                 # TODO: Clean up and remove the stream from SwarmConn if there is anything wrong.
                 self.remove_stream(net_stream)
 
-    async def _add_stream(self, muxed_stream: IMuxedStream) -> NetStream:
+    def _add_stream(self, muxed_stream: IMuxedStream) -> NetStream:
         net_stream = NetStream(muxed_stream)
         self.streams.add(net_stream)
-        await self.swarm.notify_opened_stream(net_stream)
+        self.swarm.notify_opened_stream(net_stream)
         return net_stream
 
-    async def _notify_disconnected(self) -> None:
-        await self.swarm.notify_disconnected(self)
+    def _notify_disconnected(self) -> None:
+        self.swarm.notify_disconnected(self)
 
     async def run(self) -> None:
         self.manager.run_task(self._handle_new_streams)
@@ -93,7 +93,7 @@ class SwarmConn(INetConn, Service):
 
     async def new_stream(self) -> NetStream:
         muxed_stream = await self.muxed_conn.open_stream()
-        return await self._add_stream(muxed_stream)
+        return self._add_stream(muxed_stream)
 
     async def get_streams(self) -> Tuple[NetStream, ...]:
         return tuple(self.streams)
diff --git a/libp2p/network/swarm.py b/libp2p/network/swarm.py
index 9d19717..0904774 100644
--- a/libp2p/network/swarm.py
+++ b/libp2p/network/swarm.py
@@ -250,7 +250,7 @@ class Swarm(INetworkService):
                 await listener.listen(maddr, self.manager._task_nursery)  # type: ignore
 
                 # Call notifiers since event occurred
-                await self.notify_listen(maddr)
+                self.notify_listen(maddr)
 
                 return True
             except IOError:
@@ -297,7 +297,7 @@ class Swarm(INetworkService):
         # Store muxed_conn with peer id
         self.connections[muxed_conn.peer_id] = swarm_conn
         # Call notifiers since event occurred
-        self.manager.run_task(self.notify_connected, swarm_conn)
+        self.notify_connected(swarm_conn)
         await manager.wait_started()
         return swarm_conn
 
@@ -320,27 +320,22 @@ class Swarm(INetworkService):
         """
         self.notifees.append(notifee)
 
-    # TODO: Use `run_task`.
-    async def notify_opened_stream(self, stream: INetStream) -> None:
-        async with trio.open_nursery() as nursery:
-            for notifee in self.notifees:
-                nursery.start_soon(notifee.opened_stream, self, stream)
+    def notify_opened_stream(self, stream: INetStream) -> None:
+        for notifee in self.notifees:
+            self.manager.run_task(notifee.opened_stream, self, stream)
 
     # TODO: `notify_closed_stream`
 
-    async def notify_connected(self, conn: INetConn) -> None:
-        async with trio.open_nursery() as nursery:
-            for notifee in self.notifees:
-                nursery.start_soon(notifee.connected, self, conn)
+    def notify_connected(self, conn: INetConn) -> None:
+        for notifee in self.notifees:
+            self.manager.run_task(notifee.connected, self, conn)
 
-    async def notify_disconnected(self, conn: INetConn) -> None:
-        async with trio.open_nursery() as nursery:
-            for notifee in self.notifees:
-                nursery.start_soon(notifee.disconnected, self, conn)
+    def notify_disconnected(self, conn: INetConn) -> None:
+        for notifee in self.notifees:
+            self.manager.run_task(notifee.disconnected, self, conn)
 
-    async def notify_listen(self, multiaddr: Multiaddr) -> None:
-        async with trio.open_nursery() as nursery:
-            for notifee in self.notifees:
-                nursery.start_soon(notifee.listen, self, multiaddr)
+    def notify_listen(self, multiaddr: Multiaddr) -> None:
+        for notifee in self.notifees:
+            self.manager.run_task(notifee.listen, self, multiaddr)
 
     # TODO: `notify_listen_close`