A qualitative theory of hybrid waves has been developed on a basis of a mathematical model of the chemical transformation of filtrating combustible gaseous mixture in a layer of catalytically active quiescent porous solid. The constructed mathematical model of the process includes nonlinear one-dimensional equations of. heat transfer through gas and solid phases, transfer of the mass of deficient component in the gas phase, conservation of the total amount of substance in a flow, transfer of the mass of deficient component of combustible mixture on the surface of a catalyst and ideal.-as state. Gas flows with negligible small pressure gradients have been considered. Assuming a high temperature sensitivity of chemical reaction rate and isothermicity of the elements of porous medium, the ratios have been derived for combustion wave velocity, maximum gas temperature in chemical reaction zone, equilibrium temperature and other characteristics of the process. The method of counter extrapolation has been used to estimate the structure of the hybrid wave zone. It is shown that the ratio between the specific contributions of homogeneous and heterogeneous reactions in the heat release substantially depends on the filtration velocity of the reacting gas and the coefficient of mass transfer at the interface.