diff --git a/src/codegate/providers/completion/base.py b/src/codegate/providers/completion/base.py
index 64dda954..96e68d2c 100644
--- a/src/codegate/providers/completion/base.py
+++ b/src/codegate/providers/completion/base.py
@@ -36,6 +36,10 @@ def create_response(self, response: Any) -> Union[JSONResponse, StreamingRespons
         """
         Create a FastAPI response from the completion response.
         """
-        if isinstance(response, Iterator) or inspect.isasyncgen(response):
+        if (
+            isinstance(response, Iterator)
+            or isinstance(response, AsyncIterator)
+            or inspect.isasyncgen(response)
+        ):
             return self._create_streaming_response(response)
         return self._create_json_response(response)