This paper develops the theory of liquid-gas filtration combustion, when an oxidizer (air) is injected into porous rock containing two-component liquid fuel. We found a qualitatively new combustion mechanism controlled by the successive vaporization and condensation of the liquid phase sustained by the reaction. Motivated by the problem of recovery of light oil by air injection, as an enhanced oil recovery method, we consider a liquid composed of light and medium pseudo-components. The light part is allowed to oxidize and vaporize, while the medium part is non-volatile and only oxidizes. The liquid mobility depends strongly on its composition, with a small viscosity (high mobility) of the purely light component and a high viscosity for the purely medium (immobile) component. We show that the combined vaporization and condensation in the combustion wave leads to accumulation of the light component in the upstream part of the wave, considerably increasing mobility and, therefore, playing a crucial role in the mechanism of the combustion process. We describe physical implications of this effect, as well as its importance for applications. The results are confirmed by numerical simulations. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.