Abstract: The trajectory tracking and vibration suppression control of free-floating space flexible manipulator with an attitude controlled base are discussed. With the law of conservation of momentum, the Lagrangian principle is utilized to model the dynamic function of the space flexible manipulator incorporating the assumed modes method. Using singular perturbation theory, a slow subsystem describing the rigid motion and a fast subsystem corresponding to the flexible motion are obtained. Then, a composite controller for coordinated motion between the base’s attitude and the manipulator’s joints of space flexible manipulator system is designed. The slow-subsystem partitioned neural network controller dominates the trajectory tracking of coordinated motion in joint space in the presence of unknown parameters. The fast-subsystem controller damps out the vibration of the flexible link by fuzzy logic controller. Numerical simulation results illustrate the effectiveness of the proposed controller.