Abstract: Spacecrafts are nonlinear systems. But when they are orbiting in small angles, their models correspond with Lipschitz condition. Fault detection technology could be used to insure safety of the system under these circumstances. With application of the nonlinear sliding mode method, a series of multi-channel fault detection observers for the actuators was designed. The convergence of the observers was proved by choosing a proper Lyapunov function. The observers designed for the spacecraft can realize the isolation of the faults, and this was illustrated with absurdity. The parameters of the observer were derived from the application of linear matrix inequalities. Finally, modeling and simulation were conducted for a certain satellite, and it is compared with linearization method to verify the effectiveness of the proposed algorithm.