diff --git a/synapse/handlers/presence.py b/synapse/handlers/presence.py
index 6332f50974..42fb622c48 100644
--- a/synapse/handlers/presence.py
+++ b/synapse/handlers/presence.py
@@ -135,6 +135,9 @@ class PresenceHandler(BaseHandler):
         self._remote_sendmap = {}
         # map remote users to sets of local users who're interested in them
         self._remote_recvmap = {}
+        # list of (serial, set of(userids)) tuples, ordered by serial, latest
+        # first
+        self._remote_offline_serials = []
 
         # map any user to a UserPresenceCache
         self._user_cachemap = {}
@@ -715,6 +718,10 @@ class PresenceHandler(BaseHandler):
             )
 
             if state["presence"] == PresenceState.OFFLINE:
+                self._remote_offline_serials.insert(
+                    0,
+                    (self._user_cachemap_latest_serial, set([user.to_string()]))
+                )
                 del self._user_cachemap[user]
 
         for poll in content.get("poll", []):
@@ -856,6 +863,20 @@ class PresenceEventSource(object):
 
         # TODO(paul): limit
 
+        for serial, user_ids in presence._remote_offline_serials:
+            if serial < from_key:
+                break
+
+            for u in user_ids:
+                updates.append({
+                    "type": "m.presence",
+                    "content": {"user_id": u, "presence": PresenceState.OFFLINE},
+                })
+        # TODO(paul): For the v2 API we want to tell the client their from_key
+        #   is too old if we fell off the end of the _remote_offline_serials
+        #   list, and get them to invalidate+resync. In v1 we have no such
+        #   concept so this is a best-effort result.
+
         if updates:
             defer.returnValue((updates, latest_serial))
         else:
diff --git a/tests/handlers/test_presence.py b/tests/handlers/test_presence.py
index 04eba4289e..bb497b6f09 100644
--- a/tests/handlers/test_presence.py
+++ b/tests/handlers/test_presence.py
@@ -878,6 +878,44 @@ class PresencePushTestCase(MockedDatastorePresenceTestCase):
             state
         )
 
+    @defer.inlineCallbacks
+    def test_recv_remote_offline(self):
+        """ Various tests relating to SYN-261 """
+        potato_set = self.handler._remote_recvmap.setdefault(self.u_potato,
+                set())
+        potato_set.add(self.u_apple)
+
+        self.room_members = [self.u_banana, self.u_potato]
+
+        self.assertEquals(self.event_source.get_current_key(), 0)
+
+        yield self.mock_federation_resource.trigger("PUT",
+            "/_matrix/federation/v1/send/1000000/",
+            _make_edu_json("elsewhere", "m.presence",
+                content={
+                    "push": [
+                        {"user_id": "@potato:remote",
+                         "presence": "offline"},
+                    ],
+                }
+            )
+        )
+
+        self.assertEquals(self.event_source.get_current_key(), 1)
+
+        (events, _) = yield self.event_source.get_new_events_for_user(
+            self.u_apple, 0, None
+        )
+        self.assertEquals(events,
+            [
+                {"type": "m.presence",
+                 "content": {
+                     "user_id": "@potato:remote",
+                     "presence": OFFLINE,
+                }}
+            ]
+        )
+
     @defer.inlineCallbacks
     def test_join_room_local(self):
         self.room_members = [self.u_apple, self.u_banana]