Daily activity schedules and time budgets reveal how animals cope with changing environmental conditions in securing food and evading enemies. Theory suggests that animals in populations limited by food availability should be energy maximizers in their foraging time allocation, while those regulated by predation should minimize their mobile activity levels. We compared daily and seasonal variation in activity states among three species of grazing ungulates coexisting in the same region of Kruger National Park, South Africa, and for one of these species between regions differing in rainfall. These grazers differed in body size and digestive physiology, potentially affecting their activity patterns. Hourly movement rates recorded by GPS telemetry were partitioned among activity states by applying independent mixture models. All three species showed activity peaks during the early morning and late afternoon, while resting prevailed pre-dawn as well as through midday. African buffalo showed the strongest diel variation in activity and greatest depression of midday activity, consistent with their large body size. Buffalo maintained similar levels of activity through the day and night, while zebra and sable antelope showed higher levels of diurnal than nocturnal activity. During the late dry season, zebra and coexisting sable, but not buffalo, showed elevated foraging and total mobile activity. Zebra devoted more time to foraging than both ruminants, consistent with greater food intake requirements for hindgut digestion. Sable antelope inhabiting the region with higher rainfall showed similar activity levels to the sable herd in the drier area, but slower rates of movement while foraging and travelling and less elevation in foraging time towards the end of the dry season. Observed patterns indicated subtly changing interplay among different constraints bearing on activity patterns over the diel and seasonal cycles, especially those related to digestive physiology. Simplistic concepts of energy maximization or time minimization were not supported.