diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index 518aef88..4901da4c 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -9,6 +9,8 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
   thread waker socket pair. This should improve the performance of ``wait_readable()``
   and ``wait_writable()`` when using the ``ProactorEventLoop``
   (`#836 <https://github.com/agronholm/anyio/pull/836>`_; PR by @graingert)
+- Fixed ``AssertionError`` when using ``nest-asyncio``
+  (`#840 <https://github.com/agronholm/anyio/issues/840>`_)
 
 **4.7.0**
 
diff --git a/src/anyio/_backends/_asyncio.py b/src/anyio/_backends/_asyncio.py
index 0b7479d2..5a0aa936 100644
--- a/src/anyio/_backends/_asyncio.py
+++ b/src/anyio/_backends/_asyncio.py
@@ -677,40 +677,42 @@ def __init__(self, parent_id: int | None, cancel_scope: CancelScope | None):
         self.cancel_scope = cancel_scope
 
 
-class TaskStateStore(MutableMapping["Awaitable[Any] | asyncio.Task", TaskState]):
+class TaskStateStore(
+    MutableMapping["Coroutine[Any, Any, Any] | asyncio.Task", TaskState]
+):
     def __init__(self) -> None:
         self._task_states = WeakKeyDictionary[asyncio.Task, TaskState]()
-        self._preliminary_task_states: dict[Awaitable[Any], TaskState] = {}
+        self._preliminary_task_states: dict[Coroutine[Any, Any, Any], TaskState] = {}
 
-    def __getitem__(self, key: Awaitable[Any] | asyncio.Task, /) -> TaskState:
-        assert isinstance(key, asyncio.Task)
+    def __getitem__(self, key: Coroutine[Any, Any, Any] | asyncio.Task, /) -> TaskState:
+        task = cast(asyncio.Task, key)
         try:
-            return self._task_states[key]
+            return self._task_states[task]
         except KeyError:
-            if coro := key.get_coro():
+            if coro := task.get_coro():
                 if state := self._preliminary_task_states.get(coro):
                     return state
 
         raise KeyError(key)
 
     def __setitem__(
-        self, key: asyncio.Task | Awaitable[Any], value: TaskState, /
+        self, key: asyncio.Task | Coroutine[Any, Any, Any], value: TaskState, /
     ) -> None:
-        if isinstance(key, asyncio.Task):
-            self._task_states[key] = value
-        else:
+        if isinstance(key, Coroutine):
             self._preliminary_task_states[key] = value
-
-    def __delitem__(self, key: asyncio.Task | Awaitable[Any], /) -> None:
-        if isinstance(key, asyncio.Task):
-            del self._task_states[key]
         else:
+            self._task_states[key] = value
+
+    def __delitem__(self, key: asyncio.Task | Coroutine[Any, Any, Any], /) -> None:
+        if isinstance(key, Coroutine):
             del self._preliminary_task_states[key]
+        else:
+            del self._task_states[key]
 
     def __len__(self) -> int:
         return len(self._task_states) + len(self._preliminary_task_states)
 
-    def __iter__(self) -> Iterator[Awaitable[Any] | asyncio.Task]:
+    def __iter__(self) -> Iterator[Coroutine[Any, Any, Any] | asyncio.Task]:
         yield from self._task_states
         yield from self._preliminary_task_states
 
diff --git a/tests/test_taskgroups.py b/tests/test_taskgroups.py
index 1f536940..d20565c1 100644
--- a/tests/test_taskgroups.py
+++ b/tests/test_taskgroups.py
@@ -11,7 +11,7 @@
 
 import pytest
 from exceptiongroup import catch
-from pytest import FixtureRequest
+from pytest import FixtureRequest, MonkeyPatch
 from pytest_mock import MockerFixture
 
 import anyio
@@ -1778,3 +1778,14 @@ async def sync_coro() -> None:
     async with create_task_group() as tg:
         tg.start_soon(sync_coro)
         tg.cancel_scope.cancel()
+
+
+@pytest.mark.parametrize("anyio_backend", ["asyncio"])
+async def test_patched_asyncio_task(monkeypatch: MonkeyPatch) -> None:
+    monkeypatch.setattr(
+        asyncio,
+        "Task",
+        asyncio.tasks._PyTask,  # type: ignore[attr-defined]
+    )
+    async with create_task_group() as tg:
+        tg.start_soon(sleep, 0)