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This paper presents the design, implementation, and comparative analysis of two intelligent neural network based controllers employed for nonlinear dynamic compensation and adaptive trajectory tracking of a mobile robot system. The first control law is an integration of a backstepping controller with a neural network which is designed to learn the inverse dynamic model of the robot and to compensate for the existing nonlinearities and uncertainties in the mobile robot system. This control scheme is a novel robust tracking controller which has the advantage of dealing with unmodeled and unstructured uncertainties and disturbances in the system. In the second proposed control scheme, the neural network is used to continuously tune the gains of the kinematic based controller in a backstepping structure. The online learning and adaptive capabilities of neural networks are utilized in these techniques to achieve a smooth and fast robot tracking motion. The simulation results verify the tracking performance of the proposed control algorithms over the classical backstepping controller.