diff --git a/haystack/components/generators/openai.py b/haystack/components/generators/openai.py
index 83f1a02d96..48180fc321 100644
--- a/haystack/components/generators/openai.py
+++ b/haystack/components/generators/openai.py
@@ -170,6 +170,7 @@ def from_dict(cls, data: Dict[str, Any]) -> "OpenAIGenerator":
     def run(
         self,
         prompt: str,
+        system_prompt: Optional[str] = None,
         streaming_callback: Optional[Callable[[StreamingChunk], None]] = None,
         generation_kwargs: Optional[Dict[str, Any]] = None,
     ):
@@ -178,6 +179,9 @@ def run(
 
         :param prompt:
             The string prompt to use for text generation.
+        :param system_prompt:
+            The system prompt to use for text generation. If this run time system prompt is omitted, the system
+            prompt, if defined at initialisation time, is used.
         :param streaming_callback:
             A callback function that is called when a new token is received from the stream.
         :param generation_kwargs:
@@ -189,7 +193,9 @@ def run(
         for each response.
         """
         message = ChatMessage.from_user(prompt)
-        if self.system_prompt:
+        if system_prompt is not None:
+            messages = [ChatMessage.from_system(system_prompt), message]
+        elif self.system_prompt:
             messages = [ChatMessage.from_system(self.system_prompt), message]
         else:
             messages = [message]
@@ -237,7 +243,8 @@ def run(
             "meta": [message.meta for message in completions],
         }
 
-    def _connect_chunks(self, chunk: Any, chunks: List[StreamingChunk]) -> ChatMessage:
+    @staticmethod
+    def _connect_chunks(chunk: Any, chunks: List[StreamingChunk]) -> ChatMessage:
         """
         Connects the streaming chunks into a single ChatMessage.
         """
@@ -252,7 +259,8 @@ def _connect_chunks(self, chunk: Any, chunks: List[StreamingChunk]) -> ChatMessa
         )
         return complete_response
 
-    def _build_message(self, completion: Any, choice: Any) -> ChatMessage:
+    @staticmethod
+    def _build_message(completion: Any, choice: Any) -> ChatMessage:
         """
         Converts the response from the OpenAI API to a ChatMessage.
 
@@ -276,7 +284,8 @@ def _build_message(self, completion: Any, choice: Any) -> ChatMessage:
         )
         return chat_message
 
-    def _build_chunk(self, chunk: Any) -> StreamingChunk:
+    @staticmethod
+    def _build_chunk(chunk: Any) -> StreamingChunk:
         """
         Converts the response from the OpenAI API to a StreamingChunk.
 
@@ -293,7 +302,8 @@ def _build_chunk(self, chunk: Any) -> StreamingChunk:
         chunk_message.meta.update({"model": chunk.model, "index": choice.index, "finish_reason": choice.finish_reason})
         return chunk_message
 
-    def _check_finish_reason(self, message: ChatMessage) -> None:
+    @staticmethod
+    def _check_finish_reason(message: ChatMessage) -> None:
         """
         Check the `finish_reason` returned with the OpenAI completions.
 
diff --git a/test/components/generators/test_openai.py b/test/components/generators/test_openai.py
index a164fa5e0e..047299b199 100644
--- a/test/components/generators/test_openai.py
+++ b/test/components/generators/test_openai.py
@@ -49,23 +49,6 @@ def test_init_with_parameters(self, monkeypatch):
         assert component.client.timeout == 40.0
         assert component.client.max_retries == 1
 
-    def test_init_with_parameters(self, monkeypatch):
-        monkeypatch.setenv("OPENAI_TIMEOUT", "100")
-        monkeypatch.setenv("OPENAI_MAX_RETRIES", "10")
-        component = OpenAIGenerator(
-            api_key=Secret.from_token("test-api-key"),
-            model="gpt-4o-mini",
-            streaming_callback=print_streaming_chunk,
-            api_base_url="test-base-url",
-            generation_kwargs={"max_tokens": 10, "some_test_param": "test-params"},
-        )
-        assert component.client.api_key == "test-api-key"
-        assert component.model == "gpt-4o-mini"
-        assert component.streaming_callback is print_streaming_chunk
-        assert component.generation_kwargs == {"max_tokens": 10, "some_test_param": "test-params"}
-        assert component.client.timeout == 100.0
-        assert component.client.max_retries == 10
-
     def test_to_dict_default(self, monkeypatch):
         monkeypatch.setenv("OPENAI_API_KEY", "test-api-key")
         component = OpenAIGenerator()
@@ -331,3 +314,22 @@ def __call__(self, chunk: StreamingChunk) -> None:
 
         assert callback.counter > 1
         assert "Paris" in callback.responses
+
+    @pytest.mark.skipif(
+        not os.environ.get("OPENAI_API_KEY", None),
+        reason="Export an env var called OPENAI_API_KEY containing the OpenAI API key to run this test.",
+    )
+    @pytest.mark.integration
+    def test_run_with_system_prompt(self):
+        generator = OpenAIGenerator(
+            model="gpt-4o-mini",
+            system_prompt="You answer in Portuguese, regardless of the language on which a question is asked",
+        )
+        result = generator.run("Can you explain the Pitagoras therom?")
+        assert "teorema" in result["replies"][0]
+
+        result = generator.run(
+            "Can you explain the Pitagoras therom?",
+            system_prompt="You answer in German, regardless of the language on which a question is asked.",
+        )
+        assert "Pythagoras" in result["replies"][0]