In this paper, we present the mathematical foundations of a probabilistic neural network for gene selection and classification of high-dimensional microarray data. We present a catalogue of features that a classification system for microarray data should incorporate. We then use this catalogue and compare the theoretical properties of probabilistic neural networks with support vector machines with regard to their suitability for multiclass cancer prediction. We compare the classification performance of a probabilistic neural network with the performance of a support vector machine on a multiclass microarray data set. The results of the theoretical and practical comparison suggest that the probabilistic neural network approach is to be preferred over support vector machines for multiclass cancer classification using microarray data.