diff --git a/starlette/routing.py b/starlette/routing.py
index 1c4915ffd..8043f1eb2 100644
--- a/starlette/routing.py
+++ b/starlette/routing.py
@@ -820,6 +820,7 @@ def mount(
         self, path: str, app: ASGIApp, name: typing.Optional[str] = None
     ) -> None:  # pragma: nocover
         route = Mount(path, app=app, name=name)
+        self._merge_router_events(app.router)
         self.routes.append(route)
 
     def host(
diff --git a/tests/test_applications.py b/tests/test_applications.py
index e30ec9295..e7c7f70cf 100644
--- a/tests/test_applications.py
+++ b/tests/test_applications.py
@@ -15,6 +15,7 @@
 from starlette.responses import JSONResponse, PlainTextResponse
 from starlette.routing import Host, Mount, Route, Router, WebSocketRoute
 from starlette.staticfiles import StaticFiles
+from starlette.testclient import TestClient
 from starlette.types import ASGIApp
 from starlette.websockets import WebSocket
 
@@ -281,6 +282,41 @@ def test_app_mount(tmpdir, test_client_factory):
     assert response.text == "Method Not Allowed"
 
 
+def test_app_mount_events():
+    app = Starlette()
+    nested_app = Starlette()
+
+    with pytest.warns(DeprecationWarning):
+
+        @nested_app.on_event("startup")
+        async def startup():
+            app.state.nested_started = True
+
+    app.mount(path="/", app=nested_app)
+
+    with TestClient(app):
+        assert app.state.nested_started is True
+
+
+def test_app_mount_lifespan():
+    app = Starlette()
+
+    @asynccontextmanager
+    async def lifespan(app: Starlette):
+        app.state.nested_started = True
+        yield {"router": True}
+        app.state.nested_shutdown = True
+
+    nested_app = Starlette(lifespan=lifespan)
+    app.mount(path="/", app=nested_app)
+
+    with TestClient(app):
+        assert app.state.nested_started is True
+
+    assert app.state.nested_started is True
+    assert app.state.nested_shutdown is True
+
+
 def test_app_debug(test_client_factory):
     async def homepage(request):
         raise RuntimeError()