The state-of-the-art of filtration combustion instability researches is presented. Dynamics of filtration combustion inclination instability is investigated experimentally, analytically and numerically. It is found that inclination amplitude growth velocity on the linear stage is proportional to filtration combustion wave velocity u(w), system diameter D-0 and inversed diameter of porous media particles d(0) : Delta(X) over dot similar to u(w)(D-0/d(0)).The tendency of thermal compensation of perturbation is confirmed by experiments and 2D numerical simulation. In the case of inclination growth stoppage, inclination maximum amplitude or amplitude of saturation can be estimated via the dimensionless wave velocity u and system geometrical parameters DeltaX(max) similar to (u/(1 - u))(D-0(2)/d(0)).The concept of perturbation two-staged evolution, which includes initial linear perturbation growth due to local filtration redistribution and following complex thermal and hydrodynamic reorganization of the system, is supported by experimental data and 2D simulation. (C) 2003 Elsevier Science Ltd. All rights reserved.