diff --git a/tests/test_modeling_gptj.py b/tests/test_modeling_gptj.py
index 6a6ff2240009..e94aac990bfe 100644
--- a/tests/test_modeling_gptj.py
+++ b/tests/test_modeling_gptj.py
@@ -396,8 +396,9 @@ def test_gptj_gradient_checkpointing(self):
         config_and_inputs = self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_forward_and_backwards(*config_and_inputs, gradient_checkpointing=True)
 
-    @slow
+    @tooslow
     def test_batch_generation(self):
+        # Marked as @tooslow due to GPU OOM
         model = GPTJForCausalLM.from_pretrained("EleutherAI/gpt-j-6B", revision="float16", torch_dtype=torch.float16)
         model.to(torch_device)
         tokenizer = AutoTokenizer.from_pretrained("EleutherAI/gpt-j-6B", revision="float16")
@@ -464,8 +465,9 @@ def test_model_from_pretrained(self):
 
 @require_torch
 class GPTJModelLanguageGenerationTest(unittest.TestCase):
-    @slow
+    @tooslow
     def test_lm_generate_gptj(self):
+        # Marked as @tooslow due to GPU OOM
         for checkpointing in [True, False]:
             model = GPTJForCausalLM.from_pretrained(
                 "EleutherAI/gpt-j-6B", revision="float16", torch_dtype=torch.float16