The attitude regulation problem with bounded control for a class of satellites in the presence of large disturbances, with bounded moving average, is solved using a Lyapunov-like design. The analysis and design approaches are introduced in the case in which the underlying system is an integrator and are then applied to the satellite attitude regulation problem. The performance of the resulting closed-loop systems are studied in detail and it is shown that trajectories are ultimately bounded despite the effect of the persistent disturbance. Simulation results on a model of a small satellite subject to large, but bounded in moving average, disturbances are presented.