Self-propagating high-temperature synthesis of intermetallic compounds is of wide interest. We consider reactions in a binary system in which the rise and fall of the temperature during the reaction is such that one of the reacting metals melts but not the other. For such a system, using the phase diagram of the binary system, we present a general theory that describes the reaction taking place in a single solid particle of one component surrounded by the melt of the second component. The theory gives us a set of kinetic equations that describe the propagation of the phase interfaces in the solid particle and the change in composition of the melt that surrounds it. In this article, we derive a set of equations for one- and two-layer systems in which each layer is a binary compound in the phase diagram. The system of equations is numerically solved for Al-Ni to illustrate the applicability of the theory. The method presented here is general and, depending on the complexity of the phase diagram, it could be used to obtain similar equations for systems with more layers.