This paper proposes a neural controller to guide a nonholonomic mobile robot during trajectory tracking. The structure of the controller used consists of two models that describe the kinematical mobile robot system. These models are modified Elman neural networks (MENN) and feed forward multi-layer perceptron (MLP). The modified Elman neural networks model is trained with two stages; off-line and on-line, in order to guarantee that the outputs of the model accurately represent the actual outputs of the mobile robot system. The neural model, after being trained, acts as the position and orientation predictor. The feed forward multi-layer perceptron neural networks controller is trained on-line to find the inverse kinematical model, which controls the outputs of the mobile robot system. The general back propagation algorithm is used to learn the feed forward kinematics neural controller and the predictor. The results obtained from the conducted simulation show the effectiveness of the proposed neural control algorithm. This is demonstrated by the minimized tracking error and the smoothness of the control signal obtained.