This research examines the use of neural networks in the motion control of systems involving distributed mechanical flexibility, a characteristic of large space structures systems and of high speed, high precision, light weight manipulation devices. The major problems encountered in controlling such systems are associated with dynamic nonlinearities and coupling between degrees of freedom, and with the large dynamic order of the system due to mechanical flexibility. Current control techniques, i.e., model reference adaptive control and self tuning adaptive control are based on linear systems theory. An advantage of neural networks is their ability to directly identify nonlinear dynamics and use it in the determination of the control action. A second advantage is that they are particularly suitable for systems of large dynamic order. Other useful characteristics include their learning ability and fault tolerance. In this project, the mechanical system to be controlled will be modeled in sufficient detail to provide a reasonable representation of its dynamics. The neuro-controller for the system will be trained off line to an acceptable level. It will then be installed on the actual mechanical system whose characteristics may not perfectly match those of the system on which it was trained. The control performance is expected to continuously improve by learning more and more about the system on line. The relative merits of neuro- controllers, model reference controllers, and self tuning controllers will be compared.