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This paper studies the trajectory tracking problem to control the nonlinear dynamic model of a robot using neural networks. These controllers are based on learning from input-output measurements and not on parametric-model-based dynamics. Multilayer recurrent networks are used to estimate the dynamics of the system and the inverse dynamic model. The training is achieved using the backpropagation method. The minimization of the quadratic error is computed by a variable step gradient method. Another multilayer recurrent neural network is added to estimate the joint accelerations. The control process is applied to a two degree-of-freedom (DOF) SCARA robot using a DSP-based controller. Experimental results show the effectiveness of this approach. The tracking trajectory errors are very small and torques expected at manipulator joints are free of chattering.