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A theoretical model of the decomposition of regular solid solutions under the effect of fluxes of non-equilibrium vacancies is developed. The kinetics of the redistribution of the alloy components and the shape of the stationary profiles of the components have been investigated depending on the relationship between the diffusional mobilities of the components, alloy composition, the intensities of fluxes of nonequilibrium vacancies, and the parameters that characterize the interaction of atoms of various types. It is shown that even in the range of thermodynamic stability of the alloy the allowance for the nonideality of the solid solution leads to new qualitative features in the decomposition process. In particular, the degree of decomposition increases with approaching the spinodal; the formation of regions of a fixed composition becomes possible, and in special cases, the precipitation of pure components occurs.