A moving background alters the perceived direction of target motion (the Duncker illusion). To test whether this illusion also affects pointing movements to remembered/extrapolated target locations, we constructed a display in which a target moved in a straight line and disappeared behind a band of moving random dots. Subjects were required to touch the spot where the target would emerge from the occlusion. The four directions of random-dot motion induced pointing errors that were predictable from the Duncker illusion. Because it has been previously established that saccadic direction is influenced by this illusion, gaze was subsequently recorded in a second series of experiments while subjects performed the pointing task and a similar task with eye-tracking only. In the pointing task, subjects typically saccaded to the lower border of the occlusion zone as soon as the target disappeared and then tried to maintain fixation at that spot. However, it was particularly obvious in the eye-tracking-only condition that horizontally moving random dots generally evoked an appreciable ocular following response, altering the gaze direction. Hand-pointing errors were related to the saccadic gaze error but were more highly correlated with final gaze errors (resulting from the initial saccade and the subsequent ocular following response). The results suggest a model of limb control in which gaze position can provide the target signal for limb movement.