diff --git a/src/mcp/shared/session.py b/src/mcp/shared/session.py
index 2eb184a..443527b 100644
--- a/src/mcp/shared/session.py
+++ b/src/mcp/shared/session.py
@@ -108,6 +108,7 @@ def __init__(
         receive_notification_type: type[ReceiveNotificationT],
         # If none, reading will never time out
         read_timeout_seconds: timedelta | None = None,
+        cleanup_interval_seconds: float = 60.0,
     ) -> None:
         self._read_stream = read_stream
         self._write_stream = write_stream
@@ -116,6 +117,8 @@ def __init__(
         self._receive_request_type = receive_request_type
         self._receive_notification_type = receive_notification_type
         self._read_timeout_seconds = read_timeout_seconds
+        self._cleanup_interval = cleanup_interval_seconds
+        self._in_flight: dict[RequestId, RequestResponder] = {}
 
         self._incoming_message_stream_writer, self._incoming_message_stream_reader = (
             anyio.create_memory_object_stream[
@@ -129,6 +132,7 @@ async def __aenter__(self):
         self._task_group = anyio.create_task_group()
         await self._task_group.__aenter__()
         self._task_group.start_soon(self._receive_loop)
+        self._task_group.start_soon(self._cleanup_loop)
         return self
 
     async def __aexit__(self, exc_type, exc_val, exc_tb):
@@ -221,8 +225,20 @@ async def _send_response(
             )
             await self._write_stream.send(JSONRPCMessage(jsonrpc_response))
 
+    async def _cleanup_loop(self) -> None:
+        """Periodically clean up completed and cancelled requests."""
+        while True:
+            with anyio.move_on_after(self._cleanup_interval):
+                # Clean up completed requests
+                self._in_flight = {
+                    req_id: responder
+                    for req_id, responder in self._in_flight.items()
+                    if responder.in_flight
+                }
+                await anyio.sleep(self._cleanup_interval)
+
     async def _receive_loop(self) -> None:
-        in_flight: dict[RequestId, RequestResponder] = {}
+        """Handle incoming messages and maintain request state."""
 
         async with (
             self._read_stream,
@@ -231,9 +247,9 @@ async def _receive_loop(self) -> None:
         ):
             async for message in self._read_stream:
                 # Clean up completed requests
-                in_flight = {
+                self._in_flight = {
                     req_id: responder
-                    for req_id, responder in in_flight.items()
+                    for req_id, responder in self._in_flight.items()
                     if responder.in_flight
                 }
 
@@ -257,7 +273,7 @@ async def _receive_loop(self) -> None:
                             cancel_scope=scope,
                         )
 
-                        in_flight[message.root.id] = responder
+                        self._in_flight[message.root.id] = responder
 
                         await self._received_request(responder)
                         if not responder._responded:
@@ -272,8 +288,8 @@ async def _receive_loop(self) -> None:
                     # Handle cancellation notifications
                     if isinstance(notification.root, CancelledNotification):
                         cancelled_id = notification.root.params.requestId
-                        if cancelled_id in in_flight:
-                            await in_flight[cancelled_id].cancel()
+                        if cancelled_id in self._in_flight:
+                            await self._in_flight[cancelled_id].cancel()
                     else:
                         await self._received_notification(notification)
                         await self._incoming_message_stream_writer.send(notification)