Operational problems with robots in space relate to several factors. One of the most important factors is the elastic vibrations in the joints. In this paper, control strategies for endpoint tracking of a 12.6 m×12.6 m trajectory by a two-link space robotic manipulator are reviewed. Initially, a manipulator with rigid joints is actuated using a transpose jacobian control law and a model reference adaptive control system that adapts, in real-time, the control gains in response to errors between the actual system outputs and the ideal system outputs defined by a reference model. The rigid-joint dynamics model was pursued further to study a manipulator with flexible joints modeled with linear- and nonlinear-joint stiffness models. Then, the two rigid-joint control schemes were modified using the singular perturbation-based theory and applied for the control of both linear and nonlinear flexible-joint robot models. Finally, the rigid and flexible control systems described in this paper were evaluated in numerical simulations. Simulation results suggested that greatly improved tracking accuracy can be achieved by applying the adaptive control strategies.