diff --git a/gpytorch/kernels/kernel.py b/gpytorch/kernels/kernel.py
index d2dc355dc..d4fa224a9 100644
--- a/gpytorch/kernels/kernel.py
+++ b/gpytorch/kernels/kernel.py
@@ -261,6 +261,15 @@ def batch_shape(self) -> torch.Size:
     def batch_shape(self, val: torch.Size):
         self._batch_shape = val
 
+    @property
+    def device(self) -> Optional[torch.device]:
+        if self.has_lengthscale:
+            return self.lengthscale.device
+        else:
+            for param in self.parameters():
+                return param.device
+            return None
+
     @property
     def dtype(self) -> torch.dtype:
         if self.has_lengthscale:
diff --git a/gpytorch/test/base_kernel_test_case.py b/gpytorch/test/base_kernel_test_case.py
index 793be1f0a..543759a49 100644
--- a/gpytorch/test/base_kernel_test_case.py
+++ b/gpytorch/test/base_kernel_test_case.py
@@ -179,3 +179,14 @@ def test_kernel_getitem_broadcast(self):
     def test_kernel_pickle_unpickle(self):
         kernel = self.create_kernel_no_ard(batch_shape=torch.Size([]))
         pickle.loads(pickle.dumps(kernel))  # Should be able to pickle and unpickle a kernel
+
+    def test_kernel_dtype_device(self):
+        kernel = self.create_kernel_no_ard(batch_shape=torch.Size([]))
+        self.assertEqual(kernel.dtype, torch.get_default_dtype())
+        self.assertEqual(kernel.device, torch.device("cpu"))
+        new_type = next(iter({torch.float32, torch.float64} - {torch.get_default_dtype()}))
+        kernel.to(dtype=new_type)
+        self.assertEqual(kernel.dtype, new_type)
+        if torch.cuda.is_available():
+            kernel.to(device="cuda")
+            self.assertNotEqual(kernel.device, torch.device("cpu"))