There is a renewed interest in using combustion to recover medium- or high-viscosity oil. Despite numerous experimental, numerical, and analytical studies, the mechanisms for incomplete fuel combustion or oxygen consumption are not fully understood. Incomplete oxygen consumption may lead to low-temperature oxidation reactions downstream. This paper shows that these features emerge in a relatively simple 1D model, where air is injected in a porous medium filled with inert gas, water, and an oil mixture consisting of precoke, medium oil, and light oil. Precoke is a component that is dissolved in the oil but has essentially the same composition as coke. At high temperatures, precoke is converted to coke, which participates in high-temperature oxidation. At high temperatures, medium-oil components are cracked, releasing gaseous oil. Light-oil components and water are vaporized. The model possesses an analytical solution, which was obtained by a concept introduced by Zeldovich et al. (1985). This concept, which underlies most analytical approaches such as the reaction-sheet approximation and large-activation-energy asymptotics, entails that reaction can occur only in a very small temperature range because of the highly nonlinear nature of the Arrhenius factor. For a temperature below this range, the reaction rate is too slow, and for temperatures above this range, the reaction rate is so fast that either the fuel or oxygen concentrations become zero. The model results, in the absence of external heat losses, show that there are two combustion regimes in which coke or oxygen is partially consumed. In one regime, the reaction zone moves in front of the heat wave; whereas, in the other regime, the order of the waves is reversed. There are also two combustion regimes in which the coke and oxygen are completely consumed. Also, here the reaction zone can move in front of or at the back of the heat wave. Each combustion regime is described by a sequence of waves; we derive formulas for parameters in these waves. We analyze our formulas for typical in-situ-combustion data and compare the results with numerical simulation. The main conclusion is that mainly two key parameters (i.e., the injected oxygen mole fraction and the fuel concentration) determine the combustion-front structure and when either incomplete oxygen consumption or incomplete fuel consumption occurs in the high-temperature oxidation zone.