Accurately predicting the number of faults in program modules is a major problem in the quality control of large software development efforts. Some software complexity metrics are closely related to the distribution of faults across program modules. Using these relationships, software engineers develop models that provide early estimates of quality metrics that do not become available until late in the development cycle. By considering these early estimates, software engineers can take actions to avoid or prepare for emerging quality problems. Most often, the predictive models are based upon multiple regression analysis. However, measures of software quality and complexity exhibit systematic departures from the assumptions of these analyses. With extreme violations of these assumptions, multiple regression models become unstable and lose most of their predictive quality. Since neural network models carry no data assumptions, these models could be more appropriate than regression models for modeling software faults. In this paper, we explore a neural network methodology for developing models that predict the number of faults in program modules. We apply this methodology to develop neural network models based upon data collected during the development of two commercial software systems. After developing neural network models, we apply multiple linear regression methods to develop regression models on the same data. For the data sets considered, the neural network methodology produced better predictive models in terms of both quality of fit and predictive quality.