This thesis studies the modelling of nonlinear dynaical systems using neural networks employing the system identification methodology. The most commonlyused learning algorithm for training neural network is the backpropagation algorithm. A computer program was modified and the backpropagation algotithm was used to train the multilayered perception networks. Some nonlinear dynamical examples will be trained with the backpropagation algorithm. Effect of varying with learning rates and thresholds, network complexity and some new metrics of performance were introduced.