Although an extensive body of literature exists on the cognitive underpinnings of gaze movements in macaques and humans, few studies have investigated this topic from a broader evolutionary perspective. This study used the gap–overlap paradigm to examine the timing of the gaze movements by four hominid species: humans, chimpanzees, gorillas, and orangutans. The saccade latency involved in shifting the gaze from central to peripheral stimuli was measured and compared under two conditions, gap and overlap. The central stimulus disappeared shortly before the onset of the peripheral stimulus under the gap condition, but it remained under the overlap condition. Although all species demonstrated similar saccade latencies under the gap condition, the species clearly differed from one another under the overlap condition, which may suggest their similar perceptual and motor mechanism of making a saccade on the one hand and their differential strategies for coping with the competition between two activities involving fixation and initiation of a saccade (i.e. central vs. peripheral visual stimuli) on the other hand. In particular, humans showed longer saccade latency under the overlap condition compared to the other great apes, which may reflect this species’ unique means of visual processing.