Investigation on state of the art of thermal-hydrodynamic instability of gas filtration combustion is presented. Development of the model of flow competition which takes into consideration thermal and filtration reorganization of the system as reaction to the front perturbation is proposed. Existence of characteristic and critical front inclination is demonstrated experimentally. It is shown that in the condition of experiments, characteristic inclination can be estimated by the system length and wave dimensionless velocity DeltaX(ch) similar to L . u. The inclination amplitude growth velocity is found to be proportional to wave front velocity Delta (X) over dot approximate to 0.4 . u(w).