We report a model that reproduces many of the behavioral properties of smooth pursuit eye movements. The model is a negative-feedback system that uses three parallel visual motion pathways to drive pursuit. The three visual pathways process image motion, defined as target motion with respect to the moving eye, and provide signals related to image velocity, image acceleration, and a transient that occurs at the onset of target motion. The three visual motion signals are summed and integrated to produce the eye velocity output of the model. The model reproduces the average eye velocity evoked by steps of target velocity in monkeys and humans and accounts for the variation among individual responses and subjects. When its motor pathways are expanded to include positive feedback of eye velocity and a "switch", the model reproduces the exponential decay in eye velocity observed when a moving target stops. Manipulation of this expanded model can mimic the effects of stimulation and lesions in the arcuate pursuit area, the middle temporal visual area (MT), and the medial superior temporal visual area (MST).