diff --git a/test/test_linear_expression.py b/test/test_linear_expression.py
index c3e1631c..87450586 100644
--- a/test/test_linear_expression.py
+++ b/test/test_linear_expression.py
@@ -667,6 +667,18 @@ def test_linear_expression_groupby(v, use_fallback):
     assert grouped.nterm == 10
 
 
+@pytest.mark.parametrize("use_fallback", [True])
+def test_linear_expression_groupby_ndim(z, use_fallback):
+    # TODO: implement fallback for n-dim groupby, see https://github.com/PyPSA/linopy/issues/299
+    expr = 1 * z
+    groups = xr.DataArray([[1, 1, 2], [1, 3, 3]], coords=z.coords)
+    grouped = expr.groupby(groups).sum(use_fallback=use_fallback)
+    assert "group" in grouped.dims
+    # there are three groups, 1, 2 and 3, the largest group has 3 elements
+    assert (grouped.data.group == [1, 2, 3]).all()
+    assert grouped.nterm == 3
+
+
 @pytest.mark.parametrize("use_fallback", [True, False])
 def test_linear_expression_groupby_with_name(v, use_fallback):
     expr = 1 * v