During the last two decades, evaluating severity of illness and predicting mortality of critical patients became a major concern of all professionals that work in intensive care units all over the world. Due to the binary nature of the response variable, logistic regression models were a natural choice for modelling this kind of data. The objective of this study is to compare the performance of generalized linear models (GLMs) with binary response (McCullagh and Nelder, Generalized Linear Models. Chapman and Hall, London, 1989), with the performance of generalized additive models (GAMs) with binary response (Hastie and Tibshirani, Generalized Additive Models. Chapman and Hall, New York, 1990) and also with the performance of artificial neural networks (ANNs) (Bishop, Neural Networks for Pattern Recognition. Clarendon Press, Oxford, 1995), in what concerns their predictive and discriminative power. A dataset of 996 patients was collected and the entire sample was used for the development of the models and also for the validation process, due to the nonexistence of an external, independent dataset. The performance of the proposed methodologies was assessed, not only by the evaluation of the agreement between observed mortality and predicted probabilities of death through the use of calibration plots, but also by their discriminating ability, measured by the area under the receiver operating characteristic (ROC) curve.