A system of reaction diffusion equations is considered which describes gasless combustion of condensed systems. To describe analytically recent experimental results, it is shown that a solution exhibiting a periodically pulsating, propagating reaction front arises as a Hopf bifurcation from a solution describing a uniformly propagating front. The bifurcation parameter is the product of a nondimensional activation energy and a factor which is a measure of the difference between the nondimensionalized temperatures of unburned propellant and the combustion products. It is shown that the uniformly propagating plant front is stable for parameter values below the critical value. Above the critical value the plane front becomes unstable and perturbations of the system evolve to the bifurcated state, i. e. , to the pulsating propagating state. It is also demonstrated analytically that the mean velocity of the oscillatory front is less than the velocity of the uniformly propagating plane front.