diff --git a/.gitignore b/.gitignore
index 149a9087..602f148a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -15,3 +15,5 @@ __pycache__
 .cache
 .local
 .pre-commit-config.yaml
+.vscode/
+.python-version
diff --git a/src/anyio/_backends/_asyncio.py b/src/anyio/_backends/_asyncio.py
index 68fac2ea..1c779137 100644
--- a/src/anyio/_backends/_asyncio.py
+++ b/src/anyio/_backends/_asyncio.py
@@ -233,6 +233,7 @@ def __init__(self, deadline: float = math.inf, shield: bool = False):
         self._deadline = deadline
         self._shield = shield
         self._parent_scope: Optional[CancelScope] = None
+        self._cancelled_caught = False
         self._cancel_called = False
         self._active = False
         self._timeout_handle: Optional[asyncio.TimerHandle] = None
@@ -304,6 +305,8 @@ def __exit__(self, exc_type: Optional[Type[BaseException]], exc_val: Optional[Ba
         if exc_val is not None:
             exceptions = exc_val.exceptions if isinstance(exc_val, ExceptionGroup) else [exc_val]
             if all(isinstance(exc, CancelledError) for exc in exceptions):
+                self._cancelled_caught = self._cancel_called and not self._parent_cancelled()
+
                 if self._timeout_expired:
                     return True
                 elif not self._cancel_called:
@@ -312,6 +315,8 @@ def __exit__(self, exc_type: Optional[Type[BaseException]], exc_val: Optional[Ba
                 elif not self._parent_cancelled():
                     # This scope was directly cancelled
                     return True
+        elif self._cancel_called:
+            self._cancelled_caught = True
 
         return None
 
@@ -392,6 +397,10 @@ def deadline(self, value: float) -> None:
         if self._active and not self._cancel_called:
             self._timeout()
 
+    @property
+    def cancelled_caught(self) -> bool:
+        return self._cancelled_caught
+
     @property
     def cancel_called(self) -> bool:
         return self._cancel_called
diff --git a/src/anyio/_backends/_trio.py b/src/anyio/_backends/_trio.py
index 780d3657..0778715e 100644
--- a/src/anyio/_backends/_trio.py
+++ b/src/anyio/_backends/_trio.py
@@ -85,6 +85,10 @@ def deadline(self) -> float:
     def deadline(self, value: float) -> None:
         self.__original.deadline = value
 
+    @property
+    def cancelled_caught(self) -> bool:
+        return self.__original.cancelled_caught
+
     @property
     def cancel_called(self) -> bool:
         return self.__original.cancel_called
diff --git a/src/anyio/_core/_tasks.py b/src/anyio/_core/_tasks.py
index 62230f04..5f24b434 100644
--- a/src/anyio/_core/_tasks.py
+++ b/src/anyio/_core/_tasks.py
@@ -45,6 +45,11 @@ def deadline(self) -> float:
     def deadline(self, value: float) -> None:
         raise NotImplementedError
 
+    @property
+    def cancelled_caught(self) -> bool:
+        """Records whether this scope caught a ``CancelledError``."""
+        raise NotImplementedError
+
     @property
     def cancel_called(self) -> bool:
         """``True`` if :meth:`cancel` has been called."""
diff --git a/tests/test_taskgroups.py b/tests/test_taskgroups.py
index 17abb566..130c89be 100644
--- a/tests/test_taskgroups.py
+++ b/tests/test_taskgroups.py
@@ -165,9 +165,11 @@ async def taskfunc(*, task_status):
         finished = True
 
     async def start_another():
+        nonlocal tg
         async with create_task_group() as tg:
             await tg.start(taskfunc)
 
+    tg = None
     started = finished = False
     task = asyncio.get_event_loop().create_task(start_another())
     await wait_all_tasks_blocked()
@@ -179,6 +181,34 @@ async def start_another():
     assert not finished
 
 
+@pytest.mark.parametrize('anyio_backend', ['asyncio'])
+async def test_start_native_host_cancelled_cancel_scope():
+    async def taskfunc():
+        nonlocal started, finished
+        started = True
+        await sleep(2)
+        finished = True
+
+    async def start_another():
+        nonlocal cancel_scope
+        async with CancelScope() as cancel_scope:
+            await taskfunc()
+
+    cancel_scope = None
+    started = finished = False
+    task = asyncio.get_event_loop().create_task(start_another())
+    await wait_all_tasks_blocked()
+    task.cancel()
+    with pytest.raises(asyncio.CancelledError):
+        await task
+
+    assert started
+    assert not finished
+
+    assert not cancel_scope.cancelled_caught
+    assert not cancel_scope.cancel_called
+
+
 @pytest.mark.parametrize('anyio_backend', ['asyncio'])
 async def test_start_native_child_cancelled():
     async def taskfunc(*, task_status):
@@ -395,6 +425,7 @@ async def test_fail_after(delay):
         with fail_after(delay) as scope:
             await sleep(1)
 
+    assert scope.cancelled_caught
     assert scope.cancel_called
 
 
@@ -403,6 +434,7 @@ async def test_fail_after_no_timeout():
         assert scope.deadline == float('inf')
         await sleep(0.1)
 
+    assert not scope.cancelled_caught
     assert not scope.cancel_called
 
 
@@ -429,6 +461,7 @@ async def test_move_on_after(delay):
         result = True
 
     assert not result
+    assert scope.cancelled_caught
     assert scope.cancel_called
 
 
@@ -440,6 +473,7 @@ async def test_move_on_after_no_timeout():
         result = True
 
     assert result
+    assert not scope.cancelled_caught
     assert not scope.cancel_called
 
 
@@ -456,6 +490,8 @@ async def test_nested_move_on_after():
 
     assert not sleep_completed
     assert not inner_scope_completed
+    assert outer_scope.cancelled_caught
+    assert not inner_scope.cancelled_caught
     assert outer_scope.cancel_called
     assert not inner_scope.cancel_called
 
@@ -478,6 +514,8 @@ async def cancel_when_ready():
 
     assert inner_sleep_completed
     assert not outer_sleep_completed
+    assert tg.cancel_scope.cancelled_caught
+    assert not inner_scope.cancelled_caught
     assert tg.cancel_scope.cancel_called
     assert not inner_scope.cancel_called
 
@@ -558,6 +596,7 @@ async def child():
         host_done = True
 
     assert host_done
+    assert not tg.cancel_scope.cancelled_caught
     assert not tg.cancel_scope.cancel_called
 
 
@@ -582,7 +621,11 @@ async def child(fail):
 
 
 async def test_cancel_cascade():
+    tg2 = None
+
     async def do_something():
+        nonlocal tg2
+
         async with create_task_group() as tg2:
             tg2.start_soon(sleep, 1)
 
@@ -593,6 +636,14 @@ async def do_something():
         await wait_all_tasks_blocked()
         tg.cancel_scope.cancel()
 
+        assert not tg.cancel_scope.cancelled_caught
+        assert tg.cancel_scope.cancel_called
+
+    assert tg.cancel_scope.cancelled_caught
+    assert tg.cancel_scope.cancel_called
+    assert not tg2.cancel_scope.cancelled_caught
+    assert tg2.cancel_scope.cancel_called
+
 
 async def test_cancelled_parent():
     async def child():
@@ -654,6 +705,7 @@ async def killer(scope):
 
             pytest.fail('Execution should also not reach this point')
 
+    assert scope.cancelled_caught
     assert scope.cancel_called
 
 
@@ -884,3 +936,15 @@ async def exit_scope(scope):
     with pytest.raises(RuntimeError):
         async with create_task_group() as tg:
             tg.start_soon(exit_scope, scope)
+
+
+async def test_raised():
+    class SomeExc(Exception):
+        pass
+
+    with pytest.raises(SomeExc):
+        async with CancelScope() as cancel_scope:
+            raise SomeExc
+
+    assert not cancel_scope.cancelled_caught
+    assert not cancel_scope.cancel_called