diff --git a/asyncssh/connection.py b/asyncssh/connection.py
index 9876f40..e59fff6 100644
--- a/asyncssh/connection.py
+++ b/asyncssh/connection.py
@@ -984,6 +984,7 @@ def __init__(self, loop: asyncio.AbstractEventLoop,
         self._x11_listener: Union[None, SSHX11ClientListener,
                                   SSHX11ServerListener] = None
 
+        self._tasks: Set[asyncio.Task[None]] = set()
         self._close_event = asyncio.Event()
 
         self._server_host_key_algs: Optional[Sequence[bytes]] = None
@@ -1143,6 +1144,8 @@ def _reap_task(self, task_logger: Optional[SSHLogger],
                    task: 'asyncio.Task[None]') -> None:
         """Collect result of an async task, reporting errors"""
 
+        self._tasks.discard(task)
+
         # pylint: disable=broad-except
         try:
             task.result()
@@ -1161,6 +1164,8 @@ def create_task(self, coro: Awaitable[None],
 
         task = asyncio.ensure_future(coro)
         task.add_done_callback(partial(self._reap_task, task_logger))
+        self._tasks.add(task)
+
         return task
 
     def is_client(self) -> bool: