Abstract: A kind of nonlinear dynamics model of free-floating dual-arm space robot system is based on Lagrange method, and the dynamics model of object is presented based on Newton-Euler method. Based on the results and closed kinematic chain constraints, the dynamics model of synthetical system is obtained, and the control problems for object to track the desired trajectory in workspace and adjustment of interactive forces due to the interaction between the object and the end-effectors are discussed. Because of the high complexity of structure and the uncertainty of parameter of such systems, the scheme of variable structure global sliding-mode control with better robustness to uncertainty and disturbance is proposed to track the desired trajectory of object, and the corresponded scheme of internal forces control is proposed synchronously. Therefore, the object position and internal forces can be regulated simultaneously. A fuzzy controller is designed to reduce shiver due to the inherent defect of sliding-mode control and ensure rapid response. The fuzzy controller can tune the sliding-mode control law parameters automatically according to the relationship between the system state and switch surface. The effect of the controllers is testified by computer simulation.