In this paper, global asymptotic stability of a class of nonlinear multibody flexible space structures under certain dissipative compensation is established. Furthermore, for an important subclass of such systems, the stability is shown to be robust to certain types of actuator and sensor nonlinearities. The results are applicable to robust stabilization of a wide class of systems, including flexible space structures and manipulators with articulated flexible appendages. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.