diff --git a/tests/expr_and_series/arg_max_test.py b/tests/expr_and_series/arg_max_test.py
index 56e65aff2..c8065c86f 100644
--- a/tests/expr_and_series/arg_max_test.py
+++ b/tests/expr_and_series/arg_max_test.py
@@ -19,6 +19,9 @@ def test_expr_arg_max_expr(
     if "modin" in str(constructor):
         # TODO(unassigned): bug in modin?
         return
+    if "cudf" in str(constructor):
+        # not implemented yet
+        request.applymarker(pytest.mark.xfail)
     df = nw.from_native(constructor(data))
     df = nw.maybe_set_index(df, "i")
     result = df.select(nw.col("a", "b", "z").arg_max())
@@ -31,10 +34,14 @@ def test_expr_arg_max_series(
     constructor_eager: ConstructorEager,
     col: str,
     expected: float,
+    request: pytest.FixtureRequest,
 ) -> None:
     if "modin" in str(constructor_eager):
         # TODO(unassigned): bug in modin?
         return
+    if "cudf" in str(constructor_eager):
+        # not implemented yet
+        request.applymarker(pytest.mark.xfail)
     series = nw.from_native(constructor_eager(data), eager_only=True)[col]
     series = nw.maybe_set_index(series, index=[1, 0, 9])  # type: ignore[arg-type]
     result = series.arg_max()
diff --git a/tests/expr_and_series/arg_min_test.py b/tests/expr_and_series/arg_min_test.py
index cde3b7627..99add1b83 100644
--- a/tests/expr_and_series/arg_min_test.py
+++ b/tests/expr_and_series/arg_min_test.py
@@ -16,6 +16,9 @@ def test_expr_arg_min_expr(
     if "dask" in str(constructor):
         # This operation is row-order dependent so we don't support it for Dask
         request.applymarker(pytest.mark.xfail)
+    if "cudf" in str(constructor):
+        # not implemented yet
+        request.applymarker(pytest.mark.xfail)
     df = nw.from_native(constructor(data))
     result = df.select(nw.col("a", "b", "z").arg_min())
     expected = {"a": [0], "b": [0], "z": [0]}
@@ -27,10 +30,14 @@ def test_expr_arg_min_series(
     constructor_eager: ConstructorEager,
     col: str,
     expected: float,
+    request: pytest.FixtureRequest,
 ) -> None:
     if "modin" in str(constructor_eager):
         # TODO(unassigned): bug in modin?
         return
+    if "cudf" in str(constructor_eager):
+        # not implemented yet
+        request.applymarker(pytest.mark.xfail)
     series = nw.from_native(constructor_eager(data), eager_only=True)[col]
     series = nw.maybe_set_index(series, index=[1, 0, 9])  # type: ignore[arg-type]
     result = series.arg_min()