1 Transmission over fading broadcast channels in the presence of quality of service (QoS) constraints is studied. Effective capacity, which provides the maximum constant arrival rate that a given service process can support while satisfying statistical QoS constraints, is employed as the performance metric. The effective capacity region achieved with superposition coding and successive interference cancellation is identified and is shown to be convex. Subsequently, optimal power control policies that achieve the boundary points of the effective capacity region are investigated, and an algorithm for the numerical computation of the optimal power adaptation schemes for the two-user case is provided. Additionally, performance attained with time-division multiplexing (TDM) of messages is studied for comparison with the optimal schemes.