The authors have developed the fundamentals of qualitative combustion theory involving multi-component gasless compositions on the basis of interaction effects in a multi-phase region. Using a three-component system as a model example it has been shown that the multi-phase behavior leads to a considerable expansion of combustion diversity in one and the same system due to exothermic and endothermic stages of matter redistribution between the compounds being produced, and also between one-phase and two-phase layers of a diffusive zone. In such a system one can, by varying the composition of the starting mixture, obtain various interaction regimes corresponding to (a) high or low rates of heat release, (b) monotonic or nonmonotonic temperature profiles due to matter transformation, and (c) the existence of several independent waves. For example, the second wave may be separated from the first by an endothermic stage whose zone consists of several thousand warmed-up layers.