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This paper discusses three learning algorithms to train recurrent neural networks for identification of nonlinear dynamical systems. We select memory neural networks(MNN) topology for the recurrent network in our work. MNNs are themselves dynamical systems that have internal memory obtained by adding trainable temporal elements to feed-forward networks. Three learning procedures namely back-propagation through time (BPTT), real time recurrent learning (RTRL) and extended Kalman filtering (EKF) are used for adjusting the weights in MNN to train such networks to identify the plant. The relative effectiveness of different learning algorithms have been discussed by comparing the mean square error associated with them and corresponding computational requirements. The simulation results show that RTRL algorithm is efficient for training MNNs to model nonlinear dynamical systems by considering both computational complexity and modelling accuracy. Eventhough, the accuracy of system identification is best with EKF, but it has the drawback of being computationally intensive.