Neural networks have received considerable attention recently, mostly by non-statisticians. They are considered by many to be very promising tools for classification and prediction. In this paper we present an approach to modelling censored survival data using the input-output relationship associated with a simple feed-forward neural network as the basis for a non-linear proportional hazards model. This approach can be extended to other models used with censored survival data. The proportional hazards neural network parameters are estimated using the method of maximum likelihood. These maximum likelihood based models can be compared, using readily available techniques such as the likelihood ratio test and the Akaike criterion. The neural network models are illustrated using data on the survival of men with prostatic carcinoma. A method of interpreting the neural network predictions based on the factorial contrasts is presented.