The dynamics of animal populations can be influenced directly by prevailing resources, population density, and environmental conditions, and through the delayed effects of trophic interactions and abiotic effects on habitat conditions. For large mammals, lagged effects can extend several years back in time. We attempted to establish the causal processes governing the population changes shown by 11 ungulate species counted annually over a 20-year period in South Africa's Kruger National Park. Kudu, waterbuck, warthog, sable, tsessebe, roan, and eland declined progressively in abundance after 1986, while zebra, wildebeest, impala, and giraffe maintained high abundance levels. To identify lagged influences, we used statistical probes indexing (1) inferred changes in predator abundance as a consequence of past food availability, (2) effects on habitat conditions of prior rainfall, and (3) competitor impacts on shared food resources. Multiple linear regression models were fit to estimates of annual population growth derived from the count totals subdivided among four regions. The temporal pattern of the population declines by five species was most consistent with a lagged effect from past predator food, in addition to the direct effects of seasonal rainfall. However, models including the lagged effect of prior rainfall fit nearly as well. Species that maintained high abundance responded mainly to an immediate or lagged density feedback. Changing rainfall conditions apparently affect the relative susceptibility of ungulate species to predation. Hence, the top-down interaction with predators cannot readily be disentangled from extrinsic influences on population dynamics, mediated through resources. Population declines by some species became extreme because a prolonged period of low rainfall, especially in the dry-season component, followed a doubling in the food base supporting lions, and was coupled with widened prey distribution as a consequence of the augmentation of water points by managers. Changes in population abundance within this multi-prey, generalist predator system arose from a complex interplay between changing climatic conditions, variable food production, shifting habitat conditions, varying vulnerability to predation, and spillover effects on other species.