diff --git a/array_api_compat/cupy/_aliases.py b/array_api_compat/cupy/_aliases.py
index d7e78fd..0a15e89 100644
--- a/array_api_compat/cupy/_aliases.py
+++ b/array_api_compat/cupy/_aliases.py
@@ -108,6 +108,13 @@ def asarray(
 
         return cp.array(obj, dtype=dtype, **kwargs)
 
+def sign(x: ndarray, /) -> ndarray:
+    # CuPy sign() does not propagate nans. See
+    # https://github.com/data-apis/array-api-compat/issues/136
+    out = cp.sign(x)
+    out[cp.isnan(x)] = cp.nan
+    return out
+
 # These functions are completely new here. If the library already has them
 # (i.e., numpy 2.0), use the library version instead of our wrapper.
 if hasattr(cp, 'vecdot'):
@@ -122,6 +129,6 @@ def asarray(
 __all__ = _aliases.__all__ + ['asarray', 'bool', 'acos',
                               'acosh', 'asin', 'asinh', 'atan', 'atan2',
                               'atanh', 'bitwise_left_shift', 'bitwise_invert',
-                              'bitwise_right_shift', 'concat', 'pow']
+                              'bitwise_right_shift', 'concat', 'pow', 'sign']
 
 _all_ignore = ['cp', 'get_xp']
diff --git a/array_api_compat/torch/_aliases.py b/array_api_compat/torch/_aliases.py
index a6d642e..899d94f 100644
--- a/array_api_compat/torch/_aliases.py
+++ b/array_api_compat/torch/_aliases.py
@@ -706,6 +706,21 @@ def take(x: array, indices: array, /, *, axis: Optional[int] = None, **kwargs) -
         axis = 0
     return torch.index_select(x, axis, indices, **kwargs)
 
+def sign(x: array, /) -> array:
+    # torch sign() does not support complex numbers and does not propagate
+    # nans. See https://github.com/data-apis/array-api-compat/issues/136
+    if x.dtype.is_complex:
+        out = x/torch.abs(x)
+        # sign(0) = 0 but the above formula would give nan
+        out[x == 0+0j] = 0+0j
+        return out
+    else:
+        out = torch.sign(x)
+        if x.dtype.is_floating_point:
+            out[torch.isnan(x)] = torch.nan
+        return out
+
+
 __all__ = ['result_type', 'can_cast', 'permute_dims', 'bitwise_invert',
            'newaxis', 'conj', 'add', 'atan2', 'bitwise_and',
            'bitwise_left_shift', 'bitwise_or', 'bitwise_right_shift',
@@ -719,6 +734,6 @@ def take(x: array, indices: array, /, *, axis: Optional[int] = None, **kwargs) -
            'broadcast_arrays', 'UniqueAllResult', 'UniqueCountsResult',
            'UniqueInverseResult', 'unique_all', 'unique_counts',
            'unique_inverse', 'unique_values', 'matmul', 'matrix_transpose',
-           'vecdot', 'tensordot', 'isdtype', 'take']
+           'vecdot', 'tensordot', 'isdtype', 'take', 'sign']
 
 _all_ignore = ['torch', 'get_xp']
diff --git a/cupy-xfails.txt b/cupy-xfails.txt
index a1878e9..9c865fa 100644
--- a/cupy-xfails.txt
+++ b/cupy-xfails.txt
@@ -160,7 +160,6 @@ array_api_tests/test_special_cases.py::test_unary[expm1(x_i is -0) -> -0]
 array_api_tests/test_special_cases.py::test_unary[floor(x_i is -0) -> -0]
 array_api_tests/test_special_cases.py::test_unary[log1p(x_i is -0) -> -0]
 array_api_tests/test_special_cases.py::test_unary[round(x_i is -0) -> -0]
-array_api_tests/test_special_cases.py::test_unary[sign(x_i is NaN) -> NaN]
 array_api_tests/test_special_cases.py::test_unary[sin(x_i is -0) -> -0]
 array_api_tests/test_special_cases.py::test_unary[sinh(x_i is -0) -> -0]
 array_api_tests/test_special_cases.py::test_unary[sqrt(x_i is -0) -> -0]
diff --git a/torch-xfails.txt b/torch-xfails.txt
index 577f464..aedbc4a 100644
--- a/torch-xfails.txt
+++ b/torch-xfails.txt
@@ -169,7 +169,6 @@ array_api_tests/test_special_cases.py::test_iop[__ifloordiv__(x1_i is -infinity
 array_api_tests/test_special_cases.py::test_iop[__ifloordiv__(x1_i is -infinity and isfinite(x2_i) and x2_i > 0) -> -infinity]
 array_api_tests/test_special_cases.py::test_iop[__imod__(x1_i is +0 and x2_i < 0) -> -0]
 array_api_tests/test_special_cases.py::test_iop[__imod__(x1_i is -0 and x2_i > 0) -> +0]
-array_api_tests/test_special_cases.py::test_unary[sign(x_i is NaN) -> NaN]
 
 # Float correction is not supported by pytorch
 # (https://github.com/data-apis/array-api-tests/issues/168)
@@ -186,7 +185,6 @@ array_api_tests/test_statistical_functions.py::test_sum
 array_api_tests/test_statistical_functions.py::test_prod
 
 # These functions do not yet support complex numbers
-array_api_tests/test_operators_and_elementwise_functions.py::test_sign
 array_api_tests/test_operators_and_elementwise_functions.py::test_expm1
 array_api_tests/test_operators_and_elementwise_functions.py::test_round
 array_api_tests/test_set_functions.py::test_unique_counts