diff --git a/zmq/_asyncio_selector.py b/zmq/_asyncio_selector.py
index eef0f7a5c..3118fc0d3 100644
--- a/zmq/_asyncio_selector.py
+++ b/zmq/_asyncio_selector.py
@@ -90,6 +90,7 @@ def __init__(self, real_loop: asyncio.AbstractEventLoop) -> None:
             None
         )  # type: Optional[Tuple[List[_FileDescriptorLike], List[_FileDescriptorLike]]]
         self._closing_selector = False
+        self._closed = False
         self._thread = threading.Thread(
             name="Tornado selector",
             daemon=True,
@@ -121,6 +122,8 @@ def __del__(self) -> None:
         self._waker_w.close()
 
     def close(self) -> None:
+        if self._closed:
+            return
         with self._select_cond:
             self._closing_selector = True
             self._select_cond.notify()
@@ -129,6 +132,7 @@ def close(self) -> None:
         _selector_loops.discard(self)
         self._waker_r.close()
         self._waker_w.close()
+        self._closed = True
 
     def _wake_selector(self) -> None:
         try:
diff --git a/zmq/asyncio.py b/zmq/asyncio.py
index d6e44e82b..76ecc28db 100644
--- a/zmq/asyncio.py
+++ b/zmq/asyncio.py
@@ -18,9 +18,7 @@
 from zmq import _future
 
 # registry of asyncio loop : selector thread
-_selectors: WeakKeyDictionary[
-    asyncio.AbstractEventLoop, "_zmq._asyncio_selector.SelectorThread"
-] = WeakKeyDictionary()
+_selectors: WeakKeyDictionary = WeakKeyDictionary()
 
 
 def _get_selector_windows(
@@ -53,7 +51,18 @@ def _get_selector_windows(
             # stacklevel 5 matches most likely zmq.asyncio.Context().socket()
             stacklevel=5,
         )
+
         selector = _selectors[io_loop] = SelectorThread(io_loop)
+
+        # patch loop.close to also close the selector thread
+        loop_close = io_loop.close
+
+        def _close_selector_and_loop():
+            _selectors.pop(io_loop, None)
+            selector.close()
+            loop_close()
+
+        io_loop.close = _close_selector_and_loop
         return selector
     else:
         return io_loop
@@ -120,7 +129,8 @@ def _clear_io_state(self):
 
         called once at close
         """
-        self._selector.remove_reader(self._fd)
+        if not self.io_loop.is_closed():
+            self._selector.remove_reader(self._fd)
 
 
 Poller._socket_class = Socket
diff --git a/zmq/tests/test_asyncio.py b/zmq/tests/test_asyncio.py
index ba6bac911..e88890e2b 100644
--- a/zmq/tests/test_asyncio.py
+++ b/zmq/tests/test_asyncio.py
@@ -57,8 +57,12 @@ def setUp(self):
         super(TestAsyncIOSocket, self).setUp()
 
     def tearDown(self):
-        self.loop.close()
         super().tearDown()
+        self.loop.close()
+        # verify cleanup of references to selectors
+        assert zaio._selectors == {}
+        if 'zmq._asyncio_selector' in sys.modules:
+            assert zmq._asyncio_selector._selector_loops == set()
 
     def test_socket_class(self):
         s = self.context.socket(zmq.PUSH)
@@ -432,7 +436,7 @@ def shortDescription(self):
         return doc
 
     def setUp(self):
-        self.loop = zaio.ZMQEventLoop()
+        self.loop = asyncio.new_event_loop()
         asyncio.set_event_loop(self.loop)
         super().setUp()
 
diff --git a/zmq/tests/test_retry_eintr.py b/zmq/tests/test_retry_eintr.py
index be841f948..e635f3292 100644
--- a/zmq/tests/test_retry_eintr.py
+++ b/zmq/tests/test_retry_eintr.py
@@ -17,7 +17,7 @@
 
 
 class TestEINTRSysCall(BaseZMQTestCase):
-    """ Base class for EINTR tests. """
+    """Base class for EINTR tests."""
 
     # delay for initial signal delivery
     signal_delay = 0.1