In this paper, we propose a control design method to suppress flexible appendage vibration while controlling the attitude motion of space structures simultaneously using two different actuators; one a “slow” actuator, and the other a “fast” actuator. Because the frequency of flexible appendage vibration is much higher than that of attitude motion, this system naturally exhibits a two-time-scale dynamic behavior. After describing this system as a singularly perturbed system, the control laws of each subsystem were determined to have the following properties: the slow actuator only controls the attitude motion of space structures, and the fast actuator only suppresses flexible appendage vibration. A composite state feedback control is obtained by combining the slow subsystem and fast subsystem control laws. Simulation results are presented to show the effectiveness of this control design method.