For decades the relative importance of environmental (density-independent) factors and system intrinsic feedback mechanisms (density dependence) in determining population dynamics have been debated among ecologists. Small mammal populations have been intensely studied, stimulated by the remarkable cycles that were observed in voles and lemmings in the holarctic region. More southward, small mammal populations are not cyclic and these have received less attention. Population outbreaks of small rodents in western South America and eastern Africa (such as the leaf-eared mouse Phyllotis darwini and the African multimammate rat Mastomys natalensis) are correlated with years of unusually high rainfall and increased primary production. The population dynamic patterns however appear to be very different. Both small rodents respond positively to rainfall pulses, but there are important differences in the seasonal, density-dependent and density-independent structures. In the African multimammate mouse, the density-dependent processes are of first order, suggesting a direct effect of density on population growth. The existence of delayed density-dependence in leaf-eared mouse in Chile may imply some trophic interaction with predators. In order to understand the consequences of these differences, we will investigate how demographic processes respond to environmental variability for populations having direct and delayed density-dependencies of varying strength. In addition, we need to understand the functional dependence of population growth rate on the degree of variation in demographic rates and to understand how these demographic rates have varied in the past.