Abstract: The learning process of the Feedforward Artificial Neural Networks relies on the data, though a robustness analysis of the parameter estimates of the model must be done due to the presence of outlying observations in the data. In this paper we seek the robust properties in the parameter estimates in the sense that the influence of aberrant observations or outliers in the estimate is bounded so the neural network is able to model the bulk of data. We also seek a trade off between robustness and efficiency under a Gaussian model. An adaptive learning procedure that seeks both aspects is developed. Finally we show some simulations results applied to the RESEX time series.