We present a search for electroweak production of single top quarks produced in the DZero detector at the Tevatron collider during the 1992-1995 run. After initial selections, the signal forms less than one percent of the background, and requires a powerful analysis tool to separate it from background. For this purpose, we employ the neural network package MLPfit, and train it on Monte Carlo models of two processes for the signal, and on data and MC models of seven processes for the background. Based on an analysis of singularities in the Feynman diagrams for single-top production, we have chosen an optimal set of kinematic variables as inputs to the networks. We use separate networks for each signal-background pair. For the dominant backgrounds, we have trained sequential nets. We also present a comparison of results based on conventional and neural-network analyses.