Space manipulator systems in orbit are subject to link flexibilities since they are designed to be lightweight and long reaching. Often, their joints are driven by harmonic gear-motor units, which introduce joint flexibility. Both of these types of flexibility may cause structural vibrations. To improve endpoint tracking, advanced control strategies that benefit from the knowledge of system parameters, including those describing link and joint flexibilities, are required. In this paper, first, the equations of motion of space manipulator systems whose manipulators are subject to both link and joint flexibilities are derived. Then, a parameter estimation method is developed, based on the energy balance during the motion of a flexible space manipulator. The method estimates all system parameters including those that describe both link and joint flexibilities and can reconstruct the system full dynamics required for the application of advanced control strategies. The method, developed for spatial systems, is illustrated by a planar example.