diff --git a/src/textual/dom.py b/src/textual/dom.py
index 100aed965..2adebdafe 100644
--- a/src/textual/dom.py
+++ b/src/textual/dom.py
@@ -319,7 +319,7 @@ class DOMNode(MessagePump):
 
     @classmethod
     @lru_cache(maxsize=None)
-    def _get_component_classes(cls) -> Sequence[str]:
+    def _get_component_classes(cls) -> frozenset[str]:
         """Gets the component classes for this class and inherited from bases.
 
         Component classes are inherited from base classes, unless
@@ -335,7 +335,7 @@ class DOMNode(MessagePump):
             if not base.__dict__.get("_inherit_component_classes", True):
                 break
 
-        return sorted(component_classes)
+        return frozenset(component_classes)
 
     @property
     def parent(self) -> DOMNode | None:
diff --git a/tests/test_dom.py b/tests/test_dom.py
index f366d0706..3553a4443 100644
--- a/tests/test_dom.py
+++ b/tests/test_dom.py
@@ -157,13 +157,13 @@ def test_component_classes_inheritance():
     f = F()
     f_cc = f._get_component_classes()
 
-    assert node_cc == set()
-    assert a_cc == {"a-1", "a-2"}
-    assert b_cc == {"b-1"}
-    assert c_cc == {"b-1", "c-1", "c-2"}
+    assert node_cc == []
+    assert a_cc == ["a-1", "a-2"]
+    assert b_cc == ["b-1"]
+    assert c_cc == ["b-1", "c-1", "c-2"]
     assert d_cc == c_cc
-    assert e_cc == {"b-1", "c-1", "c-2", "e-1"}
-    assert f_cc == {"f-1"}
+    assert e_cc == ["b-1", "c-1", "c-2", "e-1"]
+    assert f_cc == ["f-1"]
 
 
 @pytest.fixture