diff --git a/src/transformers/modeling_utils.py b/src/transformers/modeling_utils.py
index 68cd41895d2c..699e6fbe6ae1 100644
--- a/src/transformers/modeling_utils.py
+++ b/src/transformers/modeling_utils.py
@@ -2546,7 +2546,7 @@ def from_pretrained(
             logger.warning(
                 "You passed `quantization_config` to `from_pretrained` but the model you're loading already has a "
                 "`quantization_config` attribute and has already quantized weights. However, loading attributes"
-                " (e.g. disable_exllama, use_cuda_fp16) will be overwritten with the one you passed to `from_pretrained`. The rest will be ignored."
+                " (e.g. disable_exllama, use_cuda_fp16, max_input_length) will be overwritten with the one you passed to `from_pretrained`. The rest will be ignored."
             )
         if (
             quantization_method_from_args == QuantizationMethod.GPTQ
@@ -2556,7 +2556,11 @@ def from_pretrained(
                 raise RuntimeError("GPU is required to quantize or run quantize model.")
             elif not (is_optimum_available() and is_auto_gptq_available()):
                 raise ImportError(
-                    "Loading GPTQ quantized model requires optimum library : `pip install optimum` and auto-gptq library 'pip install auto-gptq'"
+                    "Loading a GPTQ quantized model requires optimum (`pip install optimum`) and auto-gptq library (`pip install auto-gptq`)"
+                )
+            elif version.parse(importlib.metadata.version("auto_gptq")) < version.parse("0.4.2"):
+                raise ImportError(
+                    "You need a version of auto_gptq >= 0.4.2 to use GPTQ: `pip install --upgrade auto-gptq`"
                 )
             else:
                 # Need to protect the import
diff --git a/src/transformers/utils/quantization_config.py b/src/transformers/utils/quantization_config.py
index e302d621baa1..9b698947653d 100644
--- a/src/transformers/utils/quantization_config.py
+++ b/src/transformers/utils/quantization_config.py
@@ -346,6 +346,9 @@ class GPTQConfig(QuantizationConfigMixin):
             The pad token id. Needed to prepare the dataset when `batch_size` > 1.
         disable_exllama (`bool`, *optional*, defaults to `False`):
             Whether to use exllama backend. Only works with `bits` = 4.
+        max_input_length (`int`, *optional*)
+            The maximum input length. This is needed to initialize a buffer that depends on the maximum expected input
+            length. It is specific to the exllama backend with act-order.
     """
 
     def __init__(
@@ -365,6 +368,7 @@ def __init__(
         batch_size: int = 1,
         pad_token_id: Optional[int] = None,
         disable_exllama: bool = False,
+        max_input_length: Optional[int] = None,
         **kwargs,
     ):
         self.quant_method = QuantizationMethod.GPTQ
@@ -383,11 +387,12 @@ def __init__(
         self.batch_size = batch_size
         self.pad_token_id = pad_token_id
         self.disable_exllama = disable_exllama
+        self.max_input_length = max_input_length
         self.post_init()
 
     def get_loading_attributes(self):
         attibutes_dict = copy.deepcopy(self.__dict__)
-        loading_attibutes = ["disable_exllama", "use_cuda_fp16"]
+        loading_attibutes = ["disable_exllama", "use_cuda_fp16", "max_input_length"]
         loading_attibutes_dict = {i: j for i, j in attibutes_dict.items() if i in loading_attibutes}
         return loading_attibutes_dict
 
diff --git a/tests/quantization/gptq/test_gptq.py b/tests/quantization/gptq/test_gptq.py
index c7530471fa27..d715bd56c02e 100644
--- a/tests/quantization/gptq/test_gptq.py
+++ b/tests/quantization/gptq/test_gptq.py
@@ -86,6 +86,8 @@ class GPTQTest(unittest.TestCase):
 
     EXPECTED_OUTPUTS = set()
     EXPECTED_OUTPUTS.add("Hello my name is John and I am a professional photographer. I")
+    EXPECTED_OUTPUTS.add("Hello my name is John, I am a professional photographer and I")
+    EXPECTED_OUTPUTS.add("Hello my name is John, I am a student in the University of")
     EXPECTED_OUTPUTS.add("Hello my name is John and I am a very good looking man.")
     EXPECTED_OUTPUTS.add("Hello my name is Alyson, I am a student in the")
     EXPECTED_OUTPUTS.add("Hello my name is Alyson and I am a very sweet,")
@@ -236,6 +238,82 @@ class GPTQTestDeviceMapExllama(GPTQTest):
     disable_exllama = False
 
 
+@slow
+@require_optimum
+@require_auto_gptq
+@require_torch_gpu
+@require_accelerate
+class GPTQTestActOrderExllama(unittest.TestCase):
+    """
+    Test GPTQ model with exllama kernel and desc_act=True (also known as act-order).
+    More information on those arguments here:
+    https://huggingface.co/docs/transformers/main_classes/quantization#transformers.GPTQConfig
+    """
+
+    EXPECTED_OUTPUTS = set()
+    EXPECTED_OUTPUTS.add("Hello my name is Katie and I am a 20 year")
+    model_name = "hf-internal-testing/Llama-2-7B-GPTQ"
+    revision = "gptq-4bit-128g-actorder_True"
+    input_text = "Hello my name is"
+
+    @classmethod
+    def setUpClass(cls):
+        """
+        Setup quantized model
+        """
+
+        cls.quantization_config = GPTQConfig(bits=4, disable_exllama=False, max_input_length=4028)
+        cls.quantized_model = AutoModelForCausalLM.from_pretrained(
+            cls.model_name,
+            revision=cls.revision,
+            torch_dtype=torch.float16,
+            device_map={"": 0},
+            quantization_config=cls.quantization_config,
+        )
+        cls.tokenizer = AutoTokenizer.from_pretrained(cls.model_name, use_fast=True)
+
+    def check_inference_correctness(self, model):
+        """
+        Test the generation quality of the quantized model and see that we are matching the expected output.
+        Given that we are operating on small numbers + the testing model is relatively small, we might not get
+        the same output across GPUs. So we'll generate few tokens (5-10) and check their output.
+        """
+
+        # Check that inference pass works on the model
+        encoded_input = self.tokenizer(self.input_text, return_tensors="pt")
+
+        # Check the exactness of the results
+        output_sequences = model.generate(input_ids=encoded_input["input_ids"].to(0), max_new_tokens=10)
+
+        # Get the generation
+        self.assertIn(self.tokenizer.decode(output_sequences[0], skip_special_tokens=True), self.EXPECTED_OUTPUTS)
+
+    def test_generate_quality(self):
+        """
+        Simple test to check the quality of the model by comapring the the generated tokens with the expected tokens
+        """
+        self.check_inference_correctness(self.quantized_model)
+
+    # this test will fail until the next release of optimum
+    @pytest.mark.skip
+    def test_max_input_length(self):
+        """
+        Test if the max_input_length works. It modifies the maximum input length that of the model that runs with exllama backend.
+        """
+
+        prompt = "I am in Paris and" * 1000
+        inp = self.tokenizer(prompt, return_tensors="pt").to(0)
+        self.assertTrue(inp["input_ids"].shape[1] > 4028)
+        with self.assertRaises(RuntimeError) as cm:
+            self.quantized_model.generate(**inp, num_beams=1, min_new_tokens=3, max_new_tokens=3)
+            self.assertTrue("temp_state buffer is too small" in str(cm.exception))
+
+        prompt = "I am in Paris and" * 500
+        inp = self.tokenizer(prompt, return_tensors="pt").to(0)
+        self.assertTrue(inp["input_ids"].shape[1] < 4028)
+        self.quantized_model.generate(**inp, num_beams=1, min_new_tokens=3, max_new_tokens=3)
+
+
 # fail when run all together
 @pytest.mark.skip
 @require_accelerate