diff --git a/src/transformers/trainer.py b/src/transformers/trainer.py
index 5a57fbfef5f..27652435f44 100755
--- a/src/transformers/trainer.py
+++ b/src/transformers/trainer.py
@@ -565,7 +565,7 @@ class Trainer:
             logger.info(f"Using {args.half_precision_backend} half precision backend")
 
         self.do_grad_scaling = False
-        if (args.fp16 or args.bf16) and not (args.deepspeed or is_sagemaker_mp_enabled()):
+        if (args.fp16 or args.bf16) and not (args.deepspeed or is_sagemaker_mp_enabled() or is_torch_tpu_available()):
             # deepspeed and SageMaker Model Parallel manage their own half precision
             if args.half_precision_backend == "cuda_amp":
                 self.use_cuda_amp = True
diff --git a/src/transformers/training_args.py b/src/transformers/training_args.py
index 4cb0523b404..b92afac1712 100644
--- a/src/transformers/training_args.py
+++ b/src/transformers/training_args.py
@@ -1122,9 +1122,9 @@ class TrainingArguments:
 
             if self.bf16 or self.bf16_full_eval:
 
-                if self.no_cuda and not is_torch_bf16_cpu_available():
+                if self.no_cuda and not is_torch_bf16_cpu_available() and not is_torch_tpu_available():
                     # cpu
-                    raise ValueError("Your setup doesn't support bf16/cpu. You need torch>=1.10")
+                    raise ValueError("Your setup doesn't support bf16/(cpu, tpu, neuroncore). You need torch>=1.10")
                 elif not self.no_cuda and torch.cuda.is_available() and not is_torch_bf16_gpu_available():
                     # gpu
                     raise ValueError(
@@ -1172,12 +1172,13 @@ class TrainingArguments:
             and is_torch_available()
             and (self.device.type != "cuda")
             and (get_xla_device_type(self.device) != "GPU")
+            and (get_xla_device_type(self.device) != "TPU")
             and (self.device.type != "cpu")
             and (self.bf16 or self.bf16_full_eval)
         ):
             raise ValueError(
                 "BF16 Mixed precision training with AMP (`--bf16`) and BF16 half precision evaluation"
-                " (`--bf16_full_eval`) can only be used on CUDA or CPU devices."
+                " (`--bf16_full_eval`) can only be used on CUDA or CPU/TPU/NeuronCore devices."
             )
 
         if self.torchdynamo is not None: