In this paper, we present a neural network based control scheme for end-effector path tracking control of a system consisting of a rigid micro manipulator attached at the end of a flexible macro manipulator. The objective is to suppress vibrations in the macro manipulator and at the same time achieve desired motions of the end-effector of the micro manipulator. A two-layer feedforward neural network is utilized to approximate the dynamic behavior of the macro-micro manipulator (M³) system in real time, and the controller is developed without any need for prior knowledge of the dynamics. A weight-tuning algorithm for the neural network is derived using Lyapunov stability theory. It is shown that both the path tracking error and the damped vibrations are uniformly ultimately bounded under this new control scheme. Simulation results are presented and compared to those obtained using a PD joint controller.