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The structures of the four representative dynamic neural networks (NN) are presented. In order to compare the performance of different dynamic NN in the nonlinear system identification, they are used for identification of the same nonlinear dynamic system, using the genetic algorithm (GA) to train the weights of the Elman net, the modified Elman net, internal time-delayed recurrent NN and time-delayed NN. The simulation results show the generalization ability of the four dynamic NN and provide the high precision of model of the nonlinear dynamic system. It illustrates the advantages and disadvantages of the different dynamic NN.