In the previous work, the existence of travelling waves was proven for a system of three evolutionary parital differential equations modelling combustion of light porous foam under air injection. The wave sequences appearing in the Riemann solutions were also identifed. In order to simplify the analysis, distinctions between some sequences were neglected. The analysis presented in this work may lead to an improved re-classiffcation, re-enumeration, and augmentation of the possible generic wave sequences in the solution of the combustion problem in light porous foam. We also studied numerically the hypotheses for existence of the fast combustion waves. This analysis leads to a description of a manifold in parameter space which separates di erent types of combustion. Finally, we investigated systematically, using numerical simulations, the stability of the various generic wave sequences previously identified.