African antelope may devote a large proportion of their foraging time to looking around. The factors affecting such vigilance behaviour are examined for grazing antelope, five species being studied in detail. The proportion of time spent looking decreased as species body weight increased. Within species, animals in closed habitats, those with dense vegetation, tended to spend more time in looking than did animals in the open. There was some evidence that vigilance, presumably for predators, was shared by group members, but in one species, impala, vigilance apparently increased with group size and with proximity to neighbours. Time spent looking varied with position within the group; this effect was strongest in closed habitats, where central animals tended to scan least and feed most. Vigilance increased as feeding success decreased, partly due to mutual interference between looking and feeding. The possible social, foraging and predator-detection values of vigilance are discussed. A simple model is introduced to help explain the effects of cover and to facilitate further discussion.