The evolution of Description Logics (DLs) and Propositional Dynamic Logics produced a hierar chy of decidable logics with multiple maximal el ements. It would be desirable to combine different maximal logics into one super-logic, but then in ference may turn out to be undecidable. Then it is important to characterize the decidability thresh old for these logics. In this perspective, an interest ing open question pointed out by Sattler and Vardi [Sattler and Vardi, 1999] is whether inference in a hybrid μ-calculus with restricted forms of graded modalities is decidable, and which complexity class it belongs to. In this paper we prove that this calcu lus and the corresponding are un decidable. Second, we prove undecidability results for logics that support both a transitive closure op erator over roles and number restrictions.