By using the concept of intermediate layer whose thickness is equal to zero, we obtain relations for the description of nonstationary conditions of mass exchange between multicomponent bodies. Chemical reactions and accumulation of damage play the role of nonstationary factors. Standard boundary conditions of the first, second, and third kinds and the conditions of imperfect contact (for equal chemical potentials, the diffusion flows are different) follow from the obtained relations as special cases. In the last case, the interface is a reservoir capable of accumulating or producing the diffusant. We present the conditions of mass exchange, which enable us to give correct formulations for a broad class of boundary-value problems of multicomponent diffusion. The processes of joint saturation and sublimation in three-component systems with regard for the interphase kinetics and mutual influence of elements are investigated analytically.