diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 52a87347..69e0878f 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -22,14 +22,14 @@ repos:
       - id: trailing-whitespace
 
   - repo: https://github.com/astral-sh/ruff-pre-commit
-    rev: v0.6.9
+    rev: v0.8.1
     hooks:
       - id: ruff
         args: [--fix, --show-fixes]
       - id: ruff-format
 
   - repo: https://github.com/pre-commit/mirrors-mypy
-    rev: v1.11.2
+    rev: v1.13.0
     hooks:
       - id: mypy
         additional_dependencies:
diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index 05e69a09..ce4c4db0 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -5,6 +5,8 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
 
 **UNRELEASED**
 
+- Updated ``TaskGroup`` to work with asyncio's eager task factories
+  (`#764 <https://github.com/agronholm/anyio/issues/764>`_)
 - Fixed a misleading ``ValueError`` in the context of DNS failures
   (`#815 <https://github.com/agronholm/anyio/issues/815>`_; PR by @graingert)
 - Added the ``wait_readable()`` and ``wait_writable()`` functions which will accept
diff --git a/src/anyio/_backends/_asyncio.py b/src/anyio/_backends/_asyncio.py
index fe648a6f..38b68f4d 100644
--- a/src/anyio/_backends/_asyncio.py
+++ b/src/anyio/_backends/_asyncio.py
@@ -28,6 +28,8 @@
     Collection,
     Coroutine,
     Iterable,
+    Iterator,
+    MutableMapping,
     Sequence,
 )
 from concurrent.futures import Future
@@ -351,8 +353,12 @@ def get_callable_name(func: Callable) -> str:
 
 def _task_started(task: asyncio.Task) -> bool:
     """Return ``True`` if the task has been started and has not finished."""
+    # The task coro should never be None here, as we never add finished tasks to the
+    # task list
+    coro = task.get_coro()
+    assert coro is not None
     try:
-        return getcoroutinestate(task.get_coro()) in (CORO_RUNNING, CORO_SUSPENDED)
+        return getcoroutinestate(coro) in (CORO_RUNNING, CORO_SUSPENDED)
     except AttributeError:
         # task coro is async_genenerator_asend https://bugs.python.org/issue37771
         raise Exception(f"Cannot determine if task {task} has started or not") from None
@@ -409,8 +415,10 @@ def __enter__(self) -> CancelScope:
             self._parent_scope = task_state.cancel_scope
             task_state.cancel_scope = self
             if self._parent_scope is not None:
+                # If using an eager task factory, the parent scope may not even contain
+                # the host task
                 self._parent_scope._child_scopes.add(self)
-                self._parent_scope._tasks.remove(host_task)
+                self._parent_scope._tasks.discard(host_task)
 
         self._timeout()
         self._active = True
@@ -667,7 +675,45 @@ def __init__(self, parent_id: int | None, cancel_scope: CancelScope | None):
         self.cancel_scope = cancel_scope
 
 
-_task_states: WeakKeyDictionary[asyncio.Task, TaskState] = WeakKeyDictionary()
+class TaskStateStore(MutableMapping["Awaitable[Any] | asyncio.Task", TaskState]):
+    def __init__(self) -> None:
+        self._task_states = WeakKeyDictionary[asyncio.Task, TaskState]()
+        self._preliminary_task_states: dict[Awaitable[Any], TaskState] = {}
+
+    def __getitem__(self, key: Awaitable[Any] | asyncio.Task, /) -> TaskState:
+        assert isinstance(key, asyncio.Task)
+        try:
+            return self._task_states[key]
+        except KeyError:
+            if coro := key.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, /
+    ) -> None:
+        if isinstance(key, asyncio.Task):
+            self._task_states[key] = value
+        else:
+            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:
+            del self._preliminary_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]:
+        yield from self._task_states
+        yield from self._preliminary_task_states
+
+
+_task_states = TaskStateStore()
 
 
 #
@@ -787,7 +833,7 @@ def _spawn(
         task_status_future: asyncio.Future | None = None,
     ) -> asyncio.Task:
         def task_done(_task: asyncio.Task) -> None:
-            task_state = _task_states[_task]
+            # task_state = _task_states[_task]
             assert task_state.cancel_scope is not None
             assert _task in task_state.cancel_scope._tasks
             task_state.cancel_scope._tasks.remove(_task)
@@ -844,16 +890,26 @@ def task_done(_task: asyncio.Task) -> None:
                 f"the return value ({coro!r}) is not a coroutine object"
             )
 
-        name = get_callable_name(func) if name is None else str(name)
-        task = create_task(coro, name=name)
-        task.add_done_callback(task_done)
-
         # Make the spawned task inherit the task group's cancel scope
-        _task_states[task] = TaskState(
+        _task_states[coro] = task_state = TaskState(
             parent_id=parent_id, cancel_scope=self.cancel_scope
         )
+        name = get_callable_name(func) if name is None else str(name)
+        try:
+            task = create_task(coro, name=name)
+        finally:
+            del _task_states[coro]
+
+        _task_states[task] = task_state
         self.cancel_scope._tasks.add(task)
         self._tasks.add(task)
+
+        if task.done():
+            # This can happen with eager task factories
+            task_done(task)
+        else:
+            task.add_done_callback(task_done)
+
         return task
 
     def start_soon(
@@ -2086,7 +2142,9 @@ def __init__(self, task: asyncio.Task):
         else:
             parent_id = task_state.parent_id
 
-        super().__init__(id(task), parent_id, task.get_name(), task.get_coro())
+        coro = task.get_coro()
+        assert coro is not None, "created TaskInfo from a completed Task"
+        super().__init__(id(task), parent_id, task.get_name(), coro)
         self._task = weakref.ref(task)
 
     def has_pending_cancellation(self) -> bool:
@@ -2339,10 +2397,11 @@ def create_cancel_scope(
 
     @classmethod
     def current_effective_deadline(cls) -> float:
+        if (task := current_task()) is None:
+            return math.inf
+
         try:
-            cancel_scope = _task_states[
-                current_task()  # type: ignore[index]
-            ].cancel_scope
+            cancel_scope = _task_states[task].cancel_scope
         except KeyError:
             return math.inf
 
diff --git a/src/anyio/abc/_tasks.py b/src/anyio/abc/_tasks.py
index 88aecf38..f6e5c40c 100644
--- a/src/anyio/abc/_tasks.py
+++ b/src/anyio/abc/_tasks.py
@@ -40,6 +40,12 @@ class TaskGroup(metaclass=ABCMeta):
 
     :ivar cancel_scope: the cancel scope inherited by all child tasks
     :vartype cancel_scope: CancelScope
+
+    .. note:: On asyncio, support for eager task factories is considered to be
+        **experimental**. In particular, they don't follow the usual semantics of new
+        tasks being scheduled on the next iteration of the event loop, and may thus
+        cause unexpected behavior in code that wasn't written with such semantics in
+        mind.
     """
 
     cancel_scope: CancelScope
diff --git a/tests/test_sockets.py b/tests/test_sockets.py
index a1189bb8..8965ea61 100644
--- a/tests/test_sockets.py
+++ b/tests/test_sockets.py
@@ -149,7 +149,7 @@ def _identity(v: _T) -> _T:
 )
 
 
-@_ignore_win32_resource_warnings  # type: ignore[operator]
+@_ignore_win32_resource_warnings
 class TestTCPStream:
     @pytest.fixture
     def server_sock(self, family: AnyIPAddressFamily) -> Iterator[socket.socket]:
diff --git a/tests/test_taskgroups.py b/tests/test_taskgroups.py
index 78ef9983..84101e47 100644
--- a/tests/test_taskgroups.py
+++ b/tests/test_taskgroups.py
@@ -10,7 +10,8 @@
 from typing import Any, NoReturn, cast
 
 import pytest
-from exceptiongroup import ExceptionGroup, catch
+from exceptiongroup import catch
+from pytest import FixtureRequest
 from pytest_mock import MockerFixture
 
 import anyio
@@ -783,7 +784,7 @@ async def host_agen_fn() -> AsyncGenerator[None, None]:
     host_agen = host_agen_fn()
     try:
         loop = asyncio.get_running_loop()
-        await loop.create_task(host_agen.__anext__())  # type: ignore[arg-type]
+        await loop.create_task(host_agen.__anext__())
     finally:
         await host_agen.aclose()
 
@@ -1704,3 +1705,24 @@ async def typetest_optional_status(
         task_status: TaskStatus[int] = TASK_STATUS_IGNORED,
     ) -> None:
         task_status.started(1)
+
+
+@pytest.mark.skipif(
+    sys.version_info < (3, 12),
+    reason="Eager task factories require Python 3.12",
+)
+@pytest.mark.parametrize("anyio_backend", ["asyncio"])
+async def test_eager_task_factory(request: FixtureRequest) -> None:
+    async def sync_coro() -> None:
+        # This should trigger fetching the task state
+        with CancelScope():  # noqa: ASYNC100
+            pass
+
+    loop = asyncio.get_running_loop()
+    old_task_factory = loop.get_task_factory()
+    loop.set_task_factory(asyncio.eager_task_factory)
+    request.addfinalizer(lambda: loop.set_task_factory(old_task_factory))
+
+    async with create_task_group() as tg:
+        tg.start_soon(sync_coro)
+        tg.cancel_scope.cancel()