A mathematical model is proposed which describes the dynamics and the spatial distributions of two population groups, where migration is driven by considerations of socioeconomic status. The model associates segregation with instabilities of spatially uniform mixed population states. These instabilities lead to a wide range of segregation forms including: (a) variable (weak) segregation where the population is everywhere mixed and the spatial variability is controlled by a ‘status-gap’ parameter, (b) strong segregation, where nearby neighbourhoods consists of pure (unmixed) population groups, and (c) intermediate forms involving enclaves of a pure population group in neighbourhoods of mixed population. The model associates tipping-point phenomena with the existence of an unstable mixed population state which introduces a threshold for population inversion. The model predicts that uneven invasions of one population group into another may result from interface instabilities rather than from urban heterogeneities.