The combined, effect of migration and selection in Mendelian populations has received little attention from population gene-ticists. This thesis discusses both the deterministic and stochastic aspects of a discrete generation model attributed to P.A.P. Moran. The model considers two random mating populations, between which there is migration, and within which different patterns of selection occur. The discussion of the deterministic model establishes the importance of migration and natural selection in the mainte-nance of genetic variability. A new technique is used in the mathematical analysis of the model. The analysis of the stochastic model in terms of explicit mathematical functions seems to be intractable. The thesis establishes the validity of a diffusion approximation, which is then shown to be more efficient than the discrete model for obtaining numerical results.