Analysis of a normalised backpropagation (NBP) algorithm employed in feed-forward multilayer nonlinear adaptive filters trained by backpropagation is provided. It is first shown that a degree of freedom in training of a nonlinear adaptive filter can be removed according to the relationship between the gain of the activation function, learning rate and weight matrix. The derivation of the NBP algorithm for a multilayer feed-forward neural adaptive filter is then provided based upon the minimisation of the instantaneous output error of the filter. Simulation results show that the NBP algorithm converges faster than a standard backpropagation algorithm and achieves better prediction gain when applied to nonlinear and non-stationary signals.