We prove several results on the expressive power of Lambek categorial grammars extended with Kleene star. Namely, for the systems with the omega-rule and with inductive-style axiomatisations we prove undecidability (negative) results, showing that such grammars are capable of generating some universal classes of languages. On the other hand, however, we show context-freeness for a restricted case, extending a result of Buszkowski and Palka (2008).