In the coming era of the Space Station Freedom, many robotic manipulators will be working simultaneously on various parts of the space station structure. Since each link of a manipulator is a moving body relative to other bodies, they form a tree structure of interconnected bodies. Undoutedly, many of these manipulators will possess certain degree of flexibility, at links as well as at joints. To describe accurately the dynamics of such a system in a generic way, is certainly not a trivial task. However, if we approximate each flexible link as a long slender beam and assume that flexible joints behave like torsional springs, a scalar set of equations of motion can be derived explicitly for use in real time simulation or control applications. Kinematic redundancy of manipulators has been used in control algorithms to avoid singularities, evade obstacles, minimize joint torques, manipulator kinetic energy, end effector contact forces, etc ... All of these approaches have been associated with rigid manipulators where there are no unpredictable flexible motions. When dealing with flexible manipulators, the flexibility of the system will cause undesired inaccuracy in end effector motion. However, if these manipulators are kinematically redundant, we show in this thesis that their kinematic redundancy can be used to compensate for the end effector motion inaccuracy and in many cases help damp out the vibrations. Based on our newly developed dynamic model of a system of multiple space-based flexible manipulators, control algorithms are designed to regulate the flexibility while maintaining precise tracking of the end effector trajectory. These control algorithms can either utilize a manipulator kinematic redundancy to control its flexibility or borrow other arms' motion to accomplish the same task provided that the arms are interconnected. Kinematic redundancy is also useful in optimizing the robustness of controllers. Given a manipulator's characteristics, parameter uncertainties, desired trajectories and controller design, it can be shown that under certain conditions, the tracking errors in end effector space are L\sb∞ bounded. If the manipulator is kinematically redundant, we show how its redundancy can be used to minimize these tracking error bounds and in some cases, stabilize an unstable system.