We study one-dimensional flows, when air is injected into a porous medium filled with inert gas, medium or high viscosity oil and water, giving rise to a combustion wave in a process known as high-temperature oxidation (HTO). In the oil we distinguish three pseudo-components: asphaltenes, medium and light oil. At high temperatures, the heaviest components ("precoke") are converted to coke, which undergoes combustion. Medium oil components are cracked at intermediate temperatures releasing gaseous oil. Light oil components and water are vaporized. The oxidation rate of gaseous oil components is negligible. Combustion regimes are described in the form of a sequence of waves. We develop a simple mathematical pathway based on Zeldovich's approach to provide analytical formulae for parameters in these waves. It is shown that there is a combustion regime in which either coke or oxygen are partially consumed in the combustion as well as a regime in which both are consumed completely. Each of the regimes can be subdivided in two regimes, where the reaction is either trailing or leading with respect to the thermal wave. Explicit conditions for each combustion regime are given. The structure of the oil cracking layer is investigated. Stability of the solutions is studied. We analyse our formulae for typical in situ combustion data and compare the results with numerical simulations. (C) 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.