In this paper we study a generalization of Csiszár and Kiirner's broadcast channel with confidential messages. Specifically, we consider a two-user broadcast channel with one common message and two confidential messages, one for each receiver. We establish outer bounds to the rate equivocation region of this channel. Our proposed outer bounds, together with a recently proposed achievable region, help establish the rate equivocation region of several classes of discrete memoryless broadcast channels with confidential messages. Furthermore, specializing to the general broadcast channel by removing the secrecy constraint, our proposed outer bounds reduce to new capacity outer bounds for the discrete memory broadcast channel.