diff --git a/src/array_api_extra/_statistical.py b/src/array_api_extra/_statistical.py
index f9b6f6f2..2dc7ef57 100644
--- a/src/array_api_extra/_statistical.py
+++ b/src/array_api_extra/_statistical.py
@@ -366,7 +366,9 @@ def nanmean(
         or _compat.is_cupy_namespace(xp)
         or _compat.is_dask_namespace(xp)
         or _compat.is_jax_namespace(xp)
-        or _compat.is_torch_namespace(xp)
+        or (_compat.is_torch_namespace(xp) and
+            (xp.isdtype(a.dtype, "real floating") or _compat.device(a).type != "cpu")
+        )
     ):
         return xp.nanmean(a, axis=axis)
 
@@ -418,7 +420,9 @@ def nansum(
         or _compat.is_cupy_namespace(xp)
         or _compat.is_dask_namespace(xp)
         or _compat.is_jax_namespace(xp)
-        or _compat.is_torch_namespace(xp)
+        or (_compat.is_torch_namespace(xp) and
+            (xp.isdtype(a.dtype, "real floating") or _compat.device(a).type != "cpu")
+        )
     ):
         return xp.nansum(a, axis=axis)
 
diff --git a/tests/main/test_statistical.py b/tests/main/test_statistical.py
index a8fb1ea1..83cce564 100644
--- a/tests/main/test_statistical.py
+++ b/tests/main/test_statistical.py
@@ -508,6 +508,23 @@ def test_xp(self, axis: int | None, expected_list: list[float], xp: ArrayNamespa
         expected = xp.asarray(expected_list)
         assert_equal(res, expected)
 
+    def test_complex(self, xp: ArrayNamespace):
+        a = xp.asarray(
+            [
+                [1 + 2j, complex(float("nan"), 0.0), 4 + 1j, 5 - 1j],
+                [complex(float("nan"), 0.0), -2 + 1j, 3 - 2j, -4 + 2j],
+                [2 - 1j, 1 + 3j, 3 + 2j, complex(float("nan"), 0.0)],
+            ],
+            dtype=xp.complex128,
+        )
+
+        res = nansum(a, axis=0)
+        expected = xp.asarray(
+            [3 + 1j, -1 + 4j, 10 + 1j, 1 + 1j],
+            dtype=xp.complex128,
+        )
+        assert_equal(res, expected)
+
 
 class TestNanMean:
     def test_simple(self, xp: ArrayNamespace):
@@ -570,3 +587,20 @@ def test_xp(self, axis: int | None, expected_list: list[float], xp: ArrayNamespa
         res = nanmean(a, axis=axis, xp=xp)
         expected = xp.asarray(expected_list)
         assert_equal(res, expected)
+
+    def test_complex(self, xp: ArrayNamespace):
+        a = xp.asarray(
+            [
+                [1 + 2j, complex(float("nan"), 0.0), 4 + 1j, 5 - 1j],
+                [complex(float("nan"), 0.0), -2 + 1j, 3 - 2j, -4 + 2j],
+                [2 - 1j, 1 + 3j, 3 + 2j, complex(float("nan"), 0.0)],
+            ],
+            dtype=xp.complex128,
+        )
+
+        res = nanmean(a, axis=0)
+        expected = xp.asarray(
+            [1.5 + 0.5j, -0.5 + 2j, 10 / 3 + 1j / 3, 0.5 + 0.5j],
+            dtype=xp.complex128,
+        )
+        assert_close(res, expected)