1. An integrated Geographical Information System (GIS)-Spatially Explicit Population Dynamics Model (SEPM) for investigating the dynamics of red squirrel Sciurus vulgar is and grey squirrel S. carolinensis populations in different landscapes is described. 2. Using the model, we simulated processes of reproduction, mortality and dispersal in individual populations of squirrels in habitat blocks identified within a GIS. We modelled dispersal as a process whereby individual animals moved between blocks of habitat separated by areas of unsuitable habitat. An interference model simulating the effects of competition between the grey and red squirrels was incorporated where both species occupied the same habitat blocks. 3. The model was used to investigate the spread of grey squirrels and its impact on the distribution of red squirrels in Norfolk, UK, where historical information on the decline in the red squirrel and the expansion of the grey squirrel were available. 4. We examined the effect of a range of life history scenarios differing in terms of adult mortality, juvenile mortality, fecundity, habitat carrying capacity and maximum dispersal distances. Model predictions were closest to the observed expansion of the grey squirrel and decline in the red squirrel when mortality was lower and fecundity higher than the averages recorded for the grey squirrel in the United Kingdom.