People are able to judge the current position of occluded moving objects. This operation is known as motion extrapolation. It has previously been suggested that motion extrapolation is independent of the oculomotor system. Here we revisited this question by measuring eye position while participants completed two types of motion extrapolation task. In one task, a moving visual target travelled rightwards, disappeared, then reappeared further along its trajectory. Participants discriminated correct reappearance times from incorrect (too early or too late) with a two-alternative forced-choice button press. In the second task, the target travelled rightwards behind a visible, rectangular occluder, and participants pressed a button at the time when they judged it should reappear. In both tasks, performance was significantly different under fixation as compared to free eye movement conditions. When eye movements were permitted, eye movements during occlusion were related to participants' judgements. Finally, even when participants were required to fixate, small changes in eye position around fixation (<2°) were influenced by occluded target motion. These results all indicate that overlapping systems control eye movements and judgements on motion extrapolation tasks. This has implications for understanding the mechanism underlying motion extrapolation.