Abstract: Based on Lyapunov methods, the hierarchical motion planning of free-flying dual-arm space robots for obstacle avoidance is discussed. The methods make full use of the nonholonomic nature of the system. With the momentum conversation and the Jacobian matrix, the system state equations and the control output equations for control design are established. And then the primary and secondary Liapunov functions are selected. The primary function insures the movement of the endeffectors from the start point to the end point. The secondary ascertains obstacle avoidance of the endeffectors. Combined the primary and secondary functions, the two endeffectors implement the specific movement and realize obstacle avoidance. A planar dual-arm space robot is simulated to verify the proposed methods.