The precision of smooth pursuit eye movements was described by means of a new dependent measure, the "oculomotor difference threshold" (analogous to the perceptual difference threshold) which represents the smallest difference in target velocity that produces statistically distinguishable differences in eye velocity. Oculomotor difference thresholds for constant velocity motions were largest (greater than 50% of target velocity) during the initial 200 msec of target motion, despite fairly high average gains (0.7-1.4) during the same period. Oculomotor difference thresholds declined over time. By about 600-700 msec after the onset of target motion they reached values as low as the perceptual difference thresholds measured psychophysically with the same target velocities. The similarity of the difference thresholds suggests that equally precise sensory representations of target velocity influenced perception and smooth eye movements. Nonsensory influences on smooth eye movement were also found. Smooth pursuit velocity: (1) depended on the velocity of targets in preceding trials; (2) was decreased during the initial 200 msec of target motion when the duration of motion was reduced from 1 sec to 200 msec, a result which shows that high initial pursuit velocity depends on the expectation that pursuit will continue. These effects of context and expected duration allowed the eye to achieve quickly a velocity close to that of the target it was most likely to encounter. Study of the precision of pursuit may be valuable for characterizing its sensory input, but study of the effects of the context in which a stimulus appears and the effects of expectations about future target motion may be more valuable for understanding how smooth eye movements guarantee retinal image velocities optimal for vision.