In this paper, it is shown that the conventional back-propagation (BPP) algorithm for neural network regression is robust to lever(cid:173) ages (data with :n corrupted), but not to outliers (data with y corrupted). A robust model is to model the error as a mixture of normal distribution. The influence function for this mixture model is calculated and the condition for the model to be robust to outliers is given. EM algorithm  is used to estimate the parameter. The usefulness of model selection criteria is also discussed. Illustrative simulations are performed.