diff --git a/tests/test_data_collator_completion_only.py b/tests/test_data_collator_completion_only.py
index 96813b5a82..c895a616e1 100644
--- a/tests/test_data_collator_completion_only.py
+++ b/tests/test_data_collator_completion_only.py
@@ -21,14 +21,22 @@
 
 class DataCollatorForCompletionOnlyLMTester(unittest.TestCase):
     def test_data_collator_finds_response_template_llama2_tokenizer(self):
+        # this should ideally be tested with meta-llama/Llama-2-7b-hf
         self.tokenizer = AutoTokenizer.from_pretrained("trl-internal-testing/dummy-GPT2-correct-vocab")
         self.instruction = """### System: You are a helpful assistant.
 
 ### User: How much is 2+2?
 
 ### Assistant: 2+2 equals 4"""
+        self.instruction_template = "\n### User:"
         self.response_template = "\n### Assistant:"
 
+        # GPT2Tokenizer: [198, 21017, 11787, 25] -> [11787, 25]
+        # Llama2Tokenizer: [29871, 13, 2277, 29937, 4911, 29901] -> [2277, 29937, 4911, 29901]
+        self.tokenized_instruction_w_context = self.tokenizer.encode(
+            self.instruction_template, add_special_tokens=False
+        )[2:]
+
         # GPT2Tokenizer: [198, 21017, 15286, 25] -> [15286, 25]
         # Llama2Tokenizer: [29871, 13, 2277, 29937, 4007, 22137, 29901] -> [2277, 29937, 4007, 22137, 29901]
         self.tokenized_response_w_context = self.tokenizer.encode(self.response_template, add_special_tokens=False)[2:]
@@ -42,6 +50,13 @@ def test_data_collator_finds_response_template_llama2_tokenizer(self):
         self.collator = DataCollatorForCompletionOnlyLM(self.tokenized_response_w_context, tokenizer=self.tokenizer)
         self.collator.torch_call([self.tokenized_instruction])
 
+        # Test for PR #749
+        # Pass already tokenized (w context) instruction and response both so token_ids are like in the instruction + response
+        self.collator = DataCollatorForCompletionOnlyLM(
+            self.tokenized_response_w_context, self.tokenized_instruction_w_context, tokenizer=self.tokenizer
+        )
+        self.collator.torch_call([self.tokenized_instruction])
+
     def test_data_collator_handling_of_long_sequences(self):
         self.tokenizer = AutoTokenizer.from_pretrained("trl-internal-testing/dummy-GPT2-correct-vocab")
         self.instruction = """### System: You are a helpful assistant.
diff --git a/trl/trainer/utils.py b/trl/trainer/utils.py
index 451552f14b..fa58fd3374 100644
--- a/trl/trainer/utils.py
+++ b/trl/trainer/utils.py
@@ -75,21 +75,31 @@ class DataCollatorForCompletionOnlyLM(DataCollatorForLanguageModeling):
     def __init__(
         self,
         response_template: Union[str, List[int]],
-        instruction_template: Optional[str] = None,
+        instruction_template: Union[str, List[int]] = None,
         *args,
         mlm: bool = False,
         ignore_index: int = -100,
         **kwargs,
     ):
         super().__init__(*args, mlm=mlm, **kwargs)
+
         self.instruction_template = instruction_template
+        if isinstance(instruction_template, str):
+            # The user provides a string, must tokenize
+            self.instruction_token_ids = self.tokenizer.encode(self.instruction_template, add_special_tokens=False)
+        else:
+            # The user already provides the token ids
+            self.instruction_token_ids = instruction_template
+
         self.response_template = response_template
-        self.ignore_index = ignore_index
-        if type(response_template) == list:
+        if isinstance(response_template, str):
+            # The user provides a string, must tokenize
+            self.response_token_ids = self.tokenizer.encode(self.response_template, add_special_tokens=False)
+        else:
             # The user already provides the token ids
             self.response_token_ids = response_template
-        else:
-            self.response_token_ids = self.tokenizer.encode(self.response_template, add_special_tokens=False)
+
+        self.ignore_index = ignore_index
 
     def torch_call(self, examples: List[Union[List[int], Any, Dict[str, Any]]]) -> Dict[str, Any]:
         batch = super().torch_call(examples)
@@ -142,7 +152,7 @@ def torch_call(self, examples: List[Union[List[int], Any, Dict[str, Any]]]) -> D
                     )
                     batch["labels"][i, :] = self.ignore_index
 
-                human_token_ids = self.tokenizer.encode(self.instruction_template, add_special_tokens=False)
+                human_token_ids = self.instruction_token_ids
                 for human_idx in np.where(batch["labels"][i] == human_token_ids[0])[0]:
                     # find the indexes of the start of a human answer.
                     if human_token_ids == batch["labels"][i][human_idx : human_idx + len(human_token_ids)].tolist():