Flame propagation may be influenced by thermoacoustic instabilities that develop when acoustic fluctuations of the flow, are enhanced by the heat release of the flame. The nature of these instabilities depends on the thermodynamic and transport properties of the reactive mixture. including the heat of combustion, the equivalence ratio, and the Markstein number. as well as on the acceleration of gravity. In addition. the Saffman-Taylor instability. resulting from the disparity between the viscosities of the reactant and product mixtures, influences flame propagation between two closely separated walls. Analytical formulation presented in the present study redefines previously established thermoacoustic stability regimes by taking into account the influence of the Saffman-Taylor instability. The results predict elimination of the dynamically stable planar-flame regime when the wall-separation distance is sufficiently small, which is consistent with elimination of the influence of gravity in these cases.