For mixtures of carbon materials and an inert filler, dependences of the characteristics of the filtration combustion wave on the gaseous oxidizer supply rate at a fuel content in the mixture of less than 7 wt % were obtained. The existence of a lower concentration limit for a steady-state filtration combustion wave was established. It was demonstrated that at a given intensity of heat loss, the concentration limits are determined by the reactivity of the carbon material and the oxidizer supply rate. At the effective coefficient of heat loss α = 8 W/(m2 K), effective conductivity of mixture material λ = 2 W/(m K), and air supply rate G = 0.1 m/s, the lowest fraction of carbon in the mixture at which combustion is still possible was 4.5 wt % for carbon-carbon composite, 2.5 wt % for activated birch coal, and 2.0 wt % for birch coal, the most reactive kind of carbon.