diff --git a/torchrl/data/tensor_specs.py b/torchrl/data/tensor_specs.py
index 6a1666d6daf..2089e517e00 100644
--- a/torchrl/data/tensor_specs.py
+++ b/torchrl/data/tensor_specs.py
@@ -445,6 +445,7 @@ def __eq__(self, other):
             type(self) == type(other)
             and self.low.dtype == other.low.dtype
             and self.high.dtype == other.high.dtype
+            and self.device == other.device
             and torch.isclose(self.low, other.low).all()
             and torch.isclose(self.high, other.high).all()
         )
@@ -1004,6 +1005,8 @@ class LazyStackedTensorSpec(_LazyStackedMixin[TensorSpec], TensorSpec):
     def __eq__(self, other):
         if not isinstance(other, LazyStackedTensorSpec):
             return False
+        if self.device != other.device:
+            return False
         if len(self._specs) != len(other._specs):
             return False
         for _spec1, _spec2 in zip(self._specs, other._specs):
@@ -1593,6 +1596,7 @@ def __init__(
     def __eq__(self, other):
         return (
             type(other) == type(self)
+            and self.device == other.device
             and self.shape == other.shape
             and self.space == other.space
             and self.dtype == other.dtype
@@ -2825,9 +2829,9 @@ def __eq__(self, other):
             if isinstance(other, DiscreteTensorSpec):
                 return (
                     other.n == 2
+                    and other.device == self.device
                     and other.shape == self.shape
                     and other.dtype == self.dtype
-                    and other.device == self.device
                 )
             return False
         return super().__eq__(other)
@@ -3715,7 +3719,7 @@ def __eq__(self, other):
         return (
             type(self) is type(other)
             and self.shape == other.shape
-            and self._device == other._device
+            and self.device == other.device
             and set(self._specs.keys()) == set(other._specs.keys())
             and all((self._specs[key] == spec) for (key, spec) in other._specs.items())
         )
@@ -3937,6 +3941,8 @@ def __eq__(self, other):
             return False
         if self.stack_dim != other.stack_dim:
             return False
+        if self.device != other.device:
+            return False
         for _spec1, _spec2 in zip(self._specs, other._specs):
             if _spec1 != _spec2:
                 return False