In this chapter we consider the system of equations governing compressible reacting flow. The fluid is a homogeneous mixture of two species. The evolution of the flow under the mechanical conservation laws of mass, momentum and energy is coupled to the (continuous or abrupt) conversion of the “unburnt” species to the “burnt” one. We take the simplest model of such a reaction, namely, an irreversible exothermic process. The equation of state of the fluid depends on its chemical composition. The resulting (augmented) system is still nonlinear hyperbolic (in the sense of Chapter 4) and is amenable to the GRP methodology. The basic hypotheses are presented in Section 9.1, leading to the derivation of the characteristic relations and jump conditions. In Section 9.2 we describe the classical Chapman—Jouguet model of deflagrations and detonations, and the Zeldovich—von Neumann—Döring (Z—N—D) solution is presented in Section 9.3. In Section 9.4 we study the generalized Riemann problem for the system of reacting flow. The treatment here is close to that of the basic GRP case (Section 5.1), but there are significant differences because of the reaction equation. In Section 9.5 we outline briefly the resulting GRP numerical scheme and study a physical problem of ozone decomposition.