Thus, when investigating the processes of combustion in a stream of oxidant above a layer of fuel, two problems can be distinguished: the combustion of material during blowing of the surface with a stream of oxidant [1-3], and combustion in the boundary layer behind the moving shock wave [6-7]. It has been experimentally established [2, 8, 9] that the chemical reaction above the layer of fuel is localized in a narrow zone, which we shall call the diffusion flame surface, assuming that the velocity of the reaction is determined not by kinetics, but by the rate of supply and mixing of the fuel vapor as a result of diffusion in the boundary layer. (Later, we shall show that this assumption ceases to be true'in the vicinity of the spout of the boundary layer.) In their turn, the heat- and mass-transfer in the boundary layer depend on the rate of energy release as a result of chemical action. The purpose of the present paper is the study of the mechanisms of diffusion combustion of heterogeneous systems, determination of the mass-transfer, friction, the heat flow in the fuel layer, investigation of the distribution of parameters (temperature, concentration, etc.) in the boundary layer, and the effect of heat- and mass-transfer on these distributions. At the presenttime, there exists extensive experimental information on the combustion of solid [4, i0] and liquid [8, 9] fuels. However, in the majority of theoretical investigations up to now, solid fuels have been considered, neglecting the movement originating in the fuel from interaction with the stream of oxidant [1-4, 6, 7]. In this paper, the movement originating in the liquid is taken into account, and it is shown that for a defined class of heterogeneous systems this refinement has a significant effect on the results of the solution. In the majority of calculations, performed according to existing theories, it is supposed that the thermophysical parameters of the mixture (specific heat ~{ coefficient of thermal conductivity ~) are constant in the flow and are identical for components. This assumption can lead to considerable quantitative errors as, during the combustion of many heterogeneous systems, the thermophysical parameters of the components differ by a factor of 3-4, and the mean specific heat of the mixture