Predator–prey arms races are widely speculated to underlie fast speed in terrestrial mammals. However, due to lack of empirical testing, both the specificity of any evolutionary coupling between particular predator and prey species, and the relevance of alternative food-based hypotheses of speed evolution, remain obscure. Here I examine the ecological links between the sprint speed of African savannah herbivores, their vulnerability to predators, and their diet. I show that sprint speed is strongly predicted by the vulnerability of prey to their main predators; however, the direction of the link depends on the hunting style of the predator. Speed increases with vulnerability to pursuit predators, whereas vulnerability to ambush predators is associated with particularly slow speed. These findings suggest that differential vulnerability to specific predators can indeed drive interspecific variation in speed within prey communities, but that predator hunting style influences the intensity and consistency with which selection on speed is coupled between particular species.