Although predation is an important driving force of natural selection its effects on primate evolution are still not well understood, mainly because little is known about the hunting behaviour of the primates' various predators. Here, we present data on the hunting behaviour of the leopard (Panthera pardus), a major primate predator in the Tai; forest of Ivory Coast and elsewhere. Radio-tracking data showed that forest leopards primarily hunt for monkeys on the ground during the day. Faecal analyses confirmed that primates accounted for a large proportion of the leopards' diet and revealed in detail the predation pressure exerted on the eight different monkey and one chimpanzee species. We related the species-specific predation rates to various morphological, behavioural and demographic traits that are usually considered adaptations to predation (body size, group size, group composition, reproductive behaviour, and use of forest strata). Leopard predation was most reliably associated with density, suggesting that leopards hunt primates according to abundance. Contrary to predictions, leopard predation rates were not negatively, but positively, related to body size, group size and the number of males per group, suggesting that predation by leopards did not drive the evolution of these traits in the predicted way. We discuss these findings in light of some recent experimental data and suggest that the principal effect of leopard predation has been on primates' cognitive evolution.