diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index 245cb02d..9d5f9154 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -28,6 +28,20 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
 - Emit a ``ResourceWarning`` for ``MemoryObjectReceiveStream`` and
   ``MemoryObjectSendStream`` that were garbage collected without being closed (PR by
   Andrey Kazantcev)
+- Fixed memory object stream operations incorrectly raising cancelled under certain
+  conditions where it is too late to do so:
+
+  - Fixed memory object streams dropping items when
+    ``MemoryObjectSendStream.send_nowait()`` was called immediately after cancelling the
+    scope of an ``await MemoryObjectReceiveStream.receive()`` call (`#728
+    <https://github.com/agronholm/anyio/issues/728>`_)
+
+  - Fixed ``MemoryObjectSendStream.send()`` raising cancelled despite succeeding when
+    ``MemoryObjectReceiveStream.receive_nowait()`` is called immediately after
+    cancelling the scope of the ``MemoryObjectSendStream.send()`` call (`#729
+    <https://github.com/agronholm/anyio/issues/729>`_)
+
+  (PR by Ganden Schaffner)
 
 **4.3.0**
 
diff --git a/src/anyio/streams/memory.py b/src/anyio/streams/memory.py
index b16a07a4..96f30388 100644
--- a/src/anyio/streams/memory.py
+++ b/src/anyio/streams/memory.py
@@ -11,6 +11,7 @@
     ClosedResourceError,
     EndOfStream,
     WouldBlock,
+    get_cancelled_exc_class,
 )
 from ..abc import Event, ObjectReceiveStream, ObjectSendStream
 from ..lowlevel import checkpoint
@@ -104,6 +105,11 @@ async def receive(self) -> T_co:
 
             try:
                 await receive_event.wait()
+            except get_cancelled_exc_class():
+                # Ignore the immediate cancellation if we already received an item, so
+                # as not to lose it
+                if not container:
+                    raise
             finally:
                 self._state.waiting_receivers.pop(receive_event, None)
 
@@ -230,6 +236,12 @@ async def send(self, item: T_contra) -> None:
             self._state.waiting_senders[send_event] = item
             try:
                 await send_event.wait()
+            except get_cancelled_exc_class():
+                # Ignore the immediate cancellation if we already sent the item, so as
+                # to not indicate failure despite success
+                if send_event in self._state.waiting_senders:
+                    del self._state.waiting_senders[send_event]
+                    raise
             except BaseException:
                 self._state.waiting_senders.pop(send_event, None)
                 raise