Abstract: The control problem of coordinated motion of a free-floating flexible space manipulator system is discussed. Based on the assumed mode method, the system linear momentum conversation and the Lagrange equation of second kind, the second-order nonlinear dynamic equation of the flexible space manipulator system is established. Accordingly, using the Backstepping control approach, the Backstepping control scheme is designed for coordinated motion between the base’s attitude and the joints of the free-floating flexible space manipulator system. With the proposed control scheme, the system satisfies the condition of Lyapunov stability theory, and it has global asymptotic stability. A planar free-floating flexible space manipulator system is simulated to verify the effectiveness of the proposed control scheme.