Artificial Neural Networks have captured the interest of many researchers in the last five years. As with many young fields, neural network research has been largely empirical in nature, relyingstrongly on simulationstudies ofvarious network models. Empiricism is, of course, essential to any science for it provides a body of observations allowing initial characterization of the field. Eventually, however, any maturing field must begin the process of validating empirically derived conjectures with rigorous mathematical models. It is in this way that science has always pro ceeded. It is in this way that science provides conclusions that can be used across a variety of applications. This monograph by Michael Lemmon provides just such a theoretical exploration of the role ofcompetition in Artificial Neural Networks. There is good news and bad news associated with theoretical research in neural networks. The bad news isthat such work usually requires the understanding of and bringing together of results from many seemingly disparate disciplines such as neurobiology, cognitive psychology, theory of differential equations, largc scale systems theory, computer science, and electrical engineering. The good news is that for those capable of making this synthesis, the rewards are rich as exemplified in this monograph.