There are time delays in visuomanual and oculomotor pathways, and some of these time delays may be due to the finite time required to process visual motion signals and to extract accurate information about the speed and direction of the motion. The present experiments were designed to ascertain the time required to obtain a reliable estimate of the direction of target motion. Subjects were asked to indicate the final direction of a moving target, which abruptly changed direction and shortly thereafter disappeared, by pointing to its expected emergence at the boundary of an occlusion. Subjects made small but consistent errors that overestimated the target's change in direction. These errors depended little on the amount of time the target was visible (ranging from 50 to 400 ms) after it changed direction. Pointing direction was strongly correlated with gaze, which was dominated by a saccade initiated shortly after the target changed direction. The pointing errors were explained by the fact that the saccade always intercepted the (occluded) target, but then continued in the same direction toward the boundary of the occlusion. The analysis reveals that target direction was estimated accurately even at the shortest viewing time.