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Multilayer neural networks have been used successfully in many system identification and control problems, and numerous applications have been suggested in the literature. Backpropagation is one of the standard methods used in these cases to adjust the weights/biases of the neural networks. In a recent paper (Dhaouadi and Nouri, 1999) the authors suggested the use of multilayer neural networks for the identification and control of nonlinear dynamical systems and proposed an extension of the backpropagation method. In this paper, system identification with recurrent multilayer neural networks is studied, and we present in detail the update-rules of the dynamic backpropagation method, so that it can be applied in a straightforward manner for the optimisation of the parameters of these recurrent multilayer neural networks.