The sustained propagation of a combustion front is necessary for the improved recovery of oil during an in situ combustion process. In situ combustion involves the added complexity of chemical reactions. In this paper, combustion will involve two sequential oxidation reactions. High-temperature oxidation represents proper combustion, its fuel generated by the preceding low-temperature oxidation. The interaction between the two reactions in the presence of reservoir heat losses and their overall influence on front propagation are investigated using a perturbation, analytical approach, based on the assumption of large activation energies. The places where the reactions occur are treated as spatial discontinuities for heat and mass fluxes, across which appropriate jump conditions are developed. Under certain conditions, the two reaction regions are coupled and travel coherently with the same velocity. The corresponding parameter space is delineated. The resulting common velocity is investigated as a function of the various parameters, including heat losses. The work finds application to our understanding of in-situ combustion processes and their application to oil and bitumen recovery.