This paper presents efficient computational algorithms of operational space dynamics for free-flying and for free-floating space robots. Due to the lack of the fixed base, the operational space formulation of the space robot is more complex than the fixed base robot system. By paying attention to this unique characteristic, however, the novel algorithm of the operational space dynamics for a single-serial-arm space robot is derived. Furthermore, by using the concept of the articulated-body system, recursive computation algorithms of the operational space formulation for a branching-arms on the space robot is developed. The realistic dynamic simulations are illustrated to verify the computational efficiency.