diff --git a/src/anyio/_backends/_asyncio.py b/src/anyio/_backends/_asyncio.py
index 35b0cf371..070ac8785 100644
--- a/src/anyio/_backends/_asyncio.py
+++ b/src/anyio/_backends/_asyncio.py
@@ -1452,6 +1452,7 @@ async def aclose(self) -> None:
                 self._receive_future.set_result(None)
             if self._send_future and not self._send_future.done():
                 self._send_future.set_result(None)
+        await AsyncIOBackend.checkpoint()
 
 
 class UNIXSocketStream(_RawSocketMixin, abc.UNIXSocketStream):
diff --git a/src/anyio/_backends/_trio.py b/src/anyio/_backends/_trio.py
index 2e67786e8..695b36480 100644
--- a/src/anyio/_backends/_trio.py
+++ b/src/anyio/_backends/_trio.py
@@ -466,6 +466,7 @@ async def aclose(self) -> None:
         if self._trio_socket.fileno() >= 0:
             self._closed = True
             self._trio_socket.close()
+        await trio.lowlevel.checkpoint()
 
     def _convert_socket_error(self, exc: BaseException) -> NoReturn:
         if isinstance(exc, trio.ClosedResourceError):
diff --git a/tests/test_sockets.py b/tests/test_sockets.py
index cc661b79a..cff210006 100644
--- a/tests/test_sockets.py
+++ b/tests/test_sockets.py
@@ -1581,10 +1581,26 @@ async def test_from_socket_not_connected(
         with pytest.raises(ValueError, match="the socket must be connected"):
             await UNIXSocketStream.from_socket(sock_or_fd)
 
+    @pytest.mark.skipif(
+        sys.platform == "win32", reason="UNIX sockets are not available on Windows"
+    )
+    async def test_aclose_in_cancelled_scope_raises_cancelled_exc(
+        self, server_sock: socket.socket, socket_path: Path
+    ) -> None:
+        exc = None
+        stream = await connect_unix(socket_path)
+
+        with CancelScope() as scope:
+            scope.cancel()
+            try:
+                await stream.aclose()
+            except get_cancelled_exc_class() as e:
+                exc = e
+                raise
+
+        assert exc is not None
+
 
-@pytest.mark.skipif(
-    sys.platform == "win32", reason="UNIX sockets are not available on Windows"
-)
 class TestUNIXListener:
     @pytest.fixture(
         params=[