We study the propagation of combustion waves through porous samples in which two reactions occur. The first is a gastess solid-solid reaction between two solid species in the porous solid matrix which react to synthesize a solid product. The second is a solid-gas reaction in which gas, delivered to the reaction site through the pores of the sample, reacts with one of the solid species to form gaseous products. We consider the case of counter-flow filtration, in which the direction of gas flow is opposite to the direction of propagation of the reaction wave. Our purpose in considering such systemsis that the solid-solid reaction is sometimes only weakly exothermic or even endothermic, so that propagation, and lherefore synthesis, in the absence of enhancement of the reaction rate would not be possible. Enhancement is achieved by arranging for counterflow gas filtration, which leads to the solid-gas reaction. Heat released in the solid-gas reaction raises the temperature in the combustion wave, thus increasing the solid-solid reaction rate. Using the large activation energy approximation, which describes narrow reaction zones, we determine the structure and characteristics of the combustion wave.