In this paper, a composite approach to the adaptive neural network (NN) controller is proposed for a rigid link flexible joint (RLFJ) robot manipulator with unknown nonlinearities. Based on a singular perturbation formulation of robot motion dynamics, the RLFJ robot is described by a reduced-order flexible-joint model. The concept of integral manifold is used to decompose the model into fast and slow dynamics. A composite controller is proposed to deal with the uncertainties in both fast and slow subsystems and to make the link position of the robot follow the desired trajectory. Two NNs are used to approximate two explicit nonlinear functions in two control components to alleviate the symbolic computational burden. By using Lyapunov theorem extension, the stability of the whole system has been proved. The simulation results are presented to show the effectiveness of the approach.