Control of rigid–flexible multi-body systems in space, during cooperative manipulation tasks, is studied in this paper. During such tasks, flexible members such as solar panels may vibrate. These vibrations in turn can lead to oscillatory disturbing forces on other subsystems, and consequently may produce significant errors in the position of operating end-effectors of cooperative arms. Therefore, to design and implement efficient model-based controllers for such complicated nonlinear systems, deriving an accurate dynamics model is required. On the other hand, due to practical limitations and real-time implementation, such models should demand fairly low computational complexity. In this paper, a precise dynamics model is derived by virtually partitioning the system into two rigid and flexible portions. These two portions will be assembled together to generate a proper model for controller design. Then, an adaptive hybrid suppression control (AHSC) algorithm is developed based on an appropriate variation rule of a virtual damping parameter. Finally, as a practical case study a space free-flying robot (SFFR) with flexible appendages is considered to move an object along a desired path through accurate force exertion by several cooperative end-effectors. This system includes a main rigid body equipped with thrusters, two solar panels, and two cooperative manipulators. The system also includes a third and fourth arm that act as a communication antenna and a photo capturing camera, respectively. The maneuver is deliberately planned such that flexible modes of solar panels get stimulated due to arms motion, while obtained results reveal the merits of proposed controller as will be discussed.