Diffusion in solids is a well-known phenomenon that has many consequences in technology and material science. Modelling of diffusion-controlled processes requires both a reliable theory of diffusion and reliable kinetic coefficients, as well as other thermodynamic data. Often the classical Darken theory, valid for stress-free systems with ideal vacancy source and sink activity, is generalized to multicomponent systems with ideal vacancy source and sink activity. Nazarov and Gurov presented a theory for stress-free systems with no vacancy source and sink activity. Recently we published a general theory of diffusion that accounted for the role of non-ideal vacancy source and sink activity, as well as the stress state. Since diffusion theories are tested and diffusion coefficients measured usually on diffusion couples, this paper presents evolution equations based on that general theory for a diffusion couple. In the limit, the equations of the Darken theory and the Nazarov and Gurov theory are valid for ideal vacancy source and sink activity and no vacancy source and sink activity, respectively. Simulations for binary and ternary diffusion couples demonstrate the influence of the vacancy source and sink activity and the stress state on evolution of site fraction profiles of components and vacancies, and on the Kirkendall effect.