Artificial neural networks (ANN) have their origins in efforts to produce computer models of the information processing that takes place in the brain. They have found application in a wide variety of fields such as image analysis of facial features, traffic management of underground station platforms, hand-writing verification of cheques, stock market predictions, etc. They have also been applied to computer-aided molecular design, notably protein structure prediction, and more recently ANN have been used to perform statistical tasks such as discriminant analysis and multiple linear regression in the investigation of Quantitative Structure-Activity Relationships (QSAR). We have begun a study of the properties of ANN when used to perform such multivariate statistical analyses. The most popular network used in QSAR-type applications is the multi-layer feed-forward network, also known as the back propagation multi-layer perceptron (MLP). The approaches of MLP and multiple linear regression to modelling are discussed. In order to give some insight into the operation of MLP networks we have carried out experiments with artificial data. Finally, we report two examples of MLP in computer-aided design, a QSAR analysis and the prediction of secondary protein structure.