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This article presents the description and results of the application of the algorithm for the simulation and identification of nonlinear dynamic systems using artificial neural networks (ANN) trained with the error back-propagation method (BP back-propagation) and the teacher procedure. forcing (BPTF). Several configurations of neural networks of two layers of neurons were analyzed, one hidden and the other output. The proposed neural networks have been applied to two test systems, the double pendulum dynamic system and the third order induction motor. The results obtained allow us to estimate that the neural networks that adopt BPTF are quite useful for the simulation and identification of nonlinear dynamic systems, mainly during the first time steps after the periods with which the neural networks under study were trained.