<p>Space robots play an increasingly important role in orbital servicing, including repairing, refueling, and deorbiting satellites. The space robot-target combination system must be reorientated and berthed before performing orbital service tasks. However, space combination generally has flexible appendages that affect the system control performance. Hence, this paper presents an innovative dual-observer-based composite vibration control strategy for a rigid-flexible hybrid space robot-target combination (RHSRC). The proposed strategy comprehensively addresses system uncertainties, external disturbances, and joint and panel flexibility within a singular perturbation framework. Firstly, the rigid-flexible coupling dynamics of the combined system is derived, which are decoupled into a reduced-order rigid slow subsystem and a flexible fast subsystem by using the singular perturbation theory. Further, a composite control strategy is proposed for the two subsystems to achieve high-precision trajectory tracking and vibration suppression simultaneously. For the slow subsystem, a fast finite-time extended state observer (FFESO) is designed to estimate the uncertainties, and a tanh-type nonsingular terminal sliding mode (THNTSM) controller is proposed to track desired trajectory, achieving rapid finite-time convergence and low-chattering. A modified linear ESO (LESO) is designed to estimate the uncertainties and hard-to-measure modal information in the fast system. With estimation information from the proposed LESO, an adaptive robust controller is designed for flexible motion. The closed-loop stability of both the slow and fast subsystems is demonstrated using Lyapunov theory. Simulation results demonstrate that the proposed strategy can realize high-precision trajectories while suppressing flexible vibration.</p>