diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index 516beed4..206873e5 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -7,6 +7,8 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
 
 - Fixed erroneous ``TypedAttributeLookupError`` if a typed attribute getter raises
   ``KeyError``
+- Fixed ``SocketStream.receive()`` not detecting EOF on asyncio if there is also data in
+  the read buffer (`#701 <https://github.com/agronholm/anyio/issues/701>`_)
 
 **4.3.0**
 
diff --git a/src/anyio/_backends/_asyncio.py b/src/anyio/_backends/_asyncio.py
index 7be8b1d7..db15f93d 100644
--- a/src/anyio/_backends/_asyncio.py
+++ b/src/anyio/_backends/_asyncio.py
@@ -1047,6 +1047,7 @@ class StreamProtocol(asyncio.Protocol):
     read_event: asyncio.Event
     write_event: asyncio.Event
     exception: Exception | None = None
+    is_at_eof: bool = False
 
     def connection_made(self, transport: asyncio.BaseTransport) -> None:
         self.read_queue = deque()
@@ -1068,6 +1069,7 @@ def data_received(self, data: bytes) -> None:
         self.read_event.set()
 
     def eof_received(self) -> bool | None:
+        self.is_at_eof = True
         self.read_event.set()
         return True
 
@@ -1123,15 +1125,16 @@ def _raw_socket(self) -> socket.socket:
 
     async def receive(self, max_bytes: int = 65536) -> bytes:
         with self._receive_guard:
-            await AsyncIOBackend.checkpoint()
-
             if (
                 not self._protocol.read_event.is_set()
                 and not self._transport.is_closing()
+                and not self._protocol.is_at_eof
             ):
                 self._transport.resume_reading()
                 await self._protocol.read_event.wait()
                 self._transport.pause_reading()
+            else:
+                await AsyncIOBackend.checkpoint_if_cancelled()
 
             try:
                 chunk = self._protocol.read_queue.popleft()
diff --git a/tests/test_sockets.py b/tests/test_sockets.py
index a35b5003..43c7058d 100644
--- a/tests/test_sockets.py
+++ b/tests/test_sockets.py
@@ -28,6 +28,7 @@
     BrokenResourceError,
     BusyResourceError,
     ClosedResourceError,
+    EndOfStream,
     Event,
     TypedAttributeLookupError,
     connect_tcp,
@@ -681,6 +682,29 @@ async def handle(stream: SocketStream) -> None:
 
             tg.cancel_scope.cancel()
 
+    async def test_eof_after_send(self, family: AnyIPAddressFamily) -> None:
+        """Regression test for #701."""
+        received_bytes = b""
+
+        async def handle(stream: SocketStream) -> None:
+            nonlocal received_bytes
+            async with stream:
+                received_bytes = await stream.receive()
+                with pytest.raises(EndOfStream), fail_after(1):
+                    await stream.receive()
+
+            tg.cancel_scope.cancel()
+
+        multi = await create_tcp_listener(family=family, local_host="localhost")
+        async with multi, create_task_group() as tg:
+            with socket.socket(family) as client:
+                client.connect(multi.extra(SocketAttribute.local_address))
+                client.send(b"Hello")
+                client.shutdown(socket.SHUT_WR)
+                await multi.serve(handle)
+
+        assert received_bytes == b"Hello"
+
     @skip_ipv6_mark
     @pytest.mark.skipif(
         sys.platform == "win32",