The present paper gives the view of theoretical study of diffusion processes in ternary and more component solid-state systems, caused by chemical reactions and phase growth. Internal oxidation of alloys, nitridation, borating etc. are the well-known and widely investigated processes of such type. Self-consistent theoretical model of such processes must take into account both the effect of concentration macroscopic districutions on new phase precipitation growth and precipitation reaction on concentration distribution; heterophase must be explicitly allowed for. As for binary system, diffusion theory, running into the phase growth, is well developed and completely presented in monographs, the carried out theoretical investigations of ternary systems are explicitly deficient. The first part of the review presents analysis of available theoretical studies approximately up to 1980. Ratios between various analytically solved models are discussed in detail. It is shown that they don`t satisfy to full extent the above-given requirements. More consistent, both numerically and analytically solvable models developed for the last years, are considered in the review second part. 119 refs.