A secure wireless broadcast network model is investigated, in which a source node broadcasts K confidential message flows to N user nodes, with each message intended to be decoded accurately by one user and to be kept secret from all of other users (who are thus considered to be eavesdroppers with regard to all other messages but their own). The source maintains a queue for each message flow if it is not served immediately. The channel from the source to the K users is modelled as a fading broadcast channel, and the channel state information is assumed to be known to all nodes. Two eavesdropping models are considered. For a collaborative eaves-dropping model, in which the eavesdroppers exchange their outputs, the secrecy capacity region is obtained, within which each rate vector is achieved by using a time-division scheme and a source power control policy over channel states. A throughput optimal queue length based scheduling algorithm is further derived that stabilizes all arrival rate vectors contained in the secrecy capacity region. At each packet time slot, the queue length vector determines the power control policy over the channel states at the source, and hence determines the secrecy rate allocation among users. For a non-collaborative model, in which eavesdroppers do not exchange their outputs, the time-division scheme provides an achievable secrecy rate region, and the queue length based scheduling algorithm stabilizes all arrival rate vectors in this region.