It is generally assumed that an individual of a prey species can benefit from an increase in the number of its group's members by reducing its own investment in vigilance. But what behaviour should group members adopt in relation to both the risk of being preyed upon and the individual investment in vigilance? Most models assume that individuals scan independently of one another. It is generally argued that it is more profitable for each group member owing to the cost that coordination of individual scans in non-overlapping bouts of vigilance would require. We studied the relationships between both individual and collective vigilance and group size in Defassa waterbuck, Kobus ellipsiprymnus defassa, in a population living under a predation risk. Our results confirmed that the proportion of time an individual spent in vigilance decreased with group size. However, the time during which at least one individual in the group scanned the environment (collective vigilance) increased. Analyses showed that individuals neither coordinated their scanning in an asynchronous way nor scanned independently of one another. On the contrary, scanning and non-scanning bouts were synchronized between group members, producing waves of collective vigilance. We claim that these waves are triggered by allelomimetic effects i.e. they are a phenomenon produced by an individual copying its neighbour's behaviour.