The spatial dynamics of three blowfly species was investigated using a spatially extended model of density-dependent population growth and the results indicate an overall stabilizing effect. Introduction of diffusive dispersal induced a quantitative effect of damping variation in population size on the route to a one-fixed point equilibrium in the native species, Cochliomyia macellaria. On the other hand, diffusive dispersal caused qualitative shifts in the dynamics of two invading species, Chrysomya megacephala and Chrysomya putoria. In both species diffusive dispersal can produce a qualitative shift from a two-point limit cycle to a one fixed-point dynamics. Quantitatively, dispersal also has the effect of damping oscillations in population size in the invading species.