diff --git a/tests/test_router_events.py b/tests/test_router_events.py
index 9df299cda..65f2f521c 100644
--- a/tests/test_router_events.py
+++ b/tests/test_router_events.py
@@ -241,3 +241,79 @@ def test_merged_mixed_state_lifespans() -> None:
 
     with TestClient(app) as client:
         assert client.app_state == {"router": True}
+
+
+@pytest.mark.filterwarnings(
+    r"ignore:\s*on_event is deprecated, use lifespan event handlers instead.*:DeprecationWarning"
+)
+def test_router_async_shutdown_handler(state: State) -> None:
+    """Test that async on_shutdown event handlers are called correctly, for coverage."""
+    app = FastAPI()
+
+    @app.get("/")
+    def main() -> dict[str, str]:
+        return {"message": "Hello World"}
+
+    @app.on_event("shutdown")
+    async def app_shutdown() -> None:
+        state.app_shutdown = True
+
+    assert state.app_shutdown is False
+    with TestClient(app) as client:
+        assert state.app_shutdown is False
+        response = client.get("/")
+        assert response.status_code == 200, response.text
+    assert state.app_shutdown is True
+
+
+def test_router_sync_generator_lifespan(state: State) -> None:
+    """Test that a sync generator lifespan works via _wrap_gen_lifespan_context."""
+    from collections.abc import Generator
+
+    def lifespan(app: FastAPI) -> Generator[None, None, None]:
+        state.app_startup = True
+        yield
+        state.app_shutdown = True
+
+    app = FastAPI(lifespan=lifespan)  # type: ignore[arg-type]
+
+    @app.get("/")
+    def main() -> dict[str, str]:
+        return {"message": "Hello World"}
+
+    assert state.app_startup is False
+    assert state.app_shutdown is False
+    with TestClient(app) as client:
+        assert state.app_startup is True
+        assert state.app_shutdown is False
+        response = client.get("/")
+        assert response.status_code == 200, response.text
+        assert response.json() == {"message": "Hello World"}
+    assert state.app_startup is True
+    assert state.app_shutdown is True
+
+
+def test_router_async_generator_lifespan(state: State) -> None:
+    """Test that an async generator lifespan (not wrapped) works."""
+
+    async def lifespan(app: FastAPI) -> AsyncGenerator[None, None]:
+        state.app_startup = True
+        yield
+        state.app_shutdown = True
+
+    app = FastAPI(lifespan=lifespan)  # type: ignore[arg-type]
+
+    @app.get("/")
+    def main() -> dict[str, str]:
+        return {"message": "Hello World"}
+
+    assert state.app_startup is False
+    assert state.app_shutdown is False
+    with TestClient(app) as client:
+        assert state.app_startup is True
+        assert state.app_shutdown is False
+        response = client.get("/")
+        assert response.status_code == 200, response.text
+        assert response.json() == {"message": "Hello World"}
+    assert state.app_startup is True
+    assert state.app_shutdown is True