The development of simple models for describing the population dynamics of species with overlapping generations is briefly described. The paper then presents a minimally complex simulation model for tsetse populations in which seasonally varying density-independent mortality, generally applied only to the adult stage, is combined with density dependence acting on both puparia and adults. Density dependence regulates population size within limits determined by an interaction between the strength of the density-dependent relationships and the variability of the seasonal density independence. Population data sets for Glossina palpalis and G. morsitans in Nigeria, and G. pallidipes in Kenya are adequately described by the model. Relationships discovered between the density-independent mortality and climatic variables for the Lambwe Valley data set allow predictions of population changes in other sites on the basis of their climatic conditions. Attempts to predict changes in the population of G. pallidipes in Somalia highlight the difficulties of this exercise. A tsetse's demographic response to climate may vary from region to region, making extensive predictions from local data sets difficult. There seems, however, no need to make more complex models to describe observed changes in tsetse populations.