We consider the solid state reactions α + β → ω and ω → α + β at sufficiently low temperatures so that volume diffusion is negligible and interphase boundary diffusion is rate controlling. The participating phases are assumed to have fixed compositions. The existence of a steady state reaction front (one which propagates with constant velocity and shape) is possible only for certain imposed conditions (e.g. for a range of driving forces). An analytical solution of the problem is given for the small slope approximation, and numerical solutions are investigated for the general case. Multiple solutions and re-entrant shapes are found for certain conditions. Possible applications of the present treatment include intermediate phase formation in multilayers, pearlite reversion and "pearlite-like" reactions.