Toincrease the mobility of on-orbit robotic systems, Space Free-Flying Robots (SFFR) in which one ormore manipulators are mounted on a thruster-equipped base, have been proposed. Unlike fixedbased manipulators, the robotic arms of SFFR are dynamically coupled with each other and the freeflying-base, hence the control problem becomes more challenging. In this paper, the Multiple Impedance Control (MIC) is developed,to manipulate space objects by multiple,arms of SFFR. The MIC law is based ,on the ,concept of designated ,impedances and enforces them at various ,system levels, i.e., the free-flying base, all cooperating manipulators, and the manipulated object itself. The object may include an internal angular momentum source, as is the case in most satellite manipulation tasks. The disturbance rejection characteristic of this algorithm is also studied. The result of this ,analysis reveals that the effect of ,disturbances ,substantially reduces ,through 2 appropriate tuning of the controller mass matrix gain. A system of three manipulators mounted,on a free-flying base is simulated in which ,force and torque disturbances are exerted at several points. The system dynamics ,is developed ,symbolically and the controlled system is simulated. The