diff --git a/test/lisp/emacs-lisp/rx-tests.el b/test/lisp/emacs-lisp/rx-tests.el
index 4a5919edf0..373bc9b2e3 100644
--- a/test/lisp/emacs-lisp/rx-tests.el
+++ b/test/lisp/emacs-lisp/rx-tests.el
@@ -109,5 +109,16 @@
                         (match-string 0 s))
                    "a"))))
 
+(ert-deftest rx-kleene-empty-string ()
+  ;; Test whether the repetition of empty string --that matches everywhere-- is handled correctly
+  (should (string-match (rx (zero-or-more "")) "foo"))
+  (should (string-match (rx (one-or-more "")) "foo")))
+
+(ert-deftest rx-kleene-unmatchable ()
+  ;; Test whether the repetition of regexp-unmatchable is handled correctly
+  (should (string-match (rx (zero-or-more (or))) "foo"))
+  (should-not (string-match (rx (or)) "foo"))
+  (should-not (string-match (rx (one-or-more (or))) "+")))
+
 (provide 'rx-tests)
 ;; rx-tests.el ends here.