As a step toward understanding the mechanism by which targets are selected for smooth-pursuit eye movements, we examined the behavior of the pursuit system when monkeys were presented with two discrete moving visual targets. Two rhesus monkeys were trained to select a small moving target identified by its color in the presence of a moving distractor of another color. Smooth-pursuit eye movements were quantified in terms of the latency of the eye movement and the initial eye acceleration profile. We have previously shown that the latency of smooth pursuit, which is normally around 100 ms, can be extended to 150 ms or shortened to 85 ms depending on whether there is a distractor moving in the opposite or same direction, respectively, relative to the direction of the target. We have now measured this effect for a 360 deg range of distractor directions, and distractor speeds of 5–45 deg/s. We have also examined the effect of varying the spatial separation and temporal asynchrony between target and distractor. The results indicate that the effect of the distractor on the latency of pursuit depends on its direction of motion, and its spatial and temporal proximity to the target, but depends very little on the speed of the distractor. Furthermore, under the conditions of these experiments, the direction of the eye movement that is emitted in response to two competing moving stimuli is not a vectorial combination of the stimulus motions, but is solely determined by the direction of the target. The results are consistent with a competitive model for smooth-pursuit target selection and suggest that the competition takes place at a stage of the pursuit pathway that is between visual-motion processing and motor-response preparation.