A stability analysis of a ramjet combustor is presented. The analysis focusses on a situation for which experimental data are available. The Mach number is low, pressure oscillations are large, and frequencies are lower than acoustics. The flame oscillates and goes through the exhaust nozzle during part of each cycle. The data are consistent with a slow modulation of the total mass of mixture in the system. This bulk oscillation interferes with entropy modes of oscillation and may destabilize them. A multiple time scale analysis is developed. It decouples to some extent the fast mechanisms:​ acoustics and flame motion, from the slow bulk/entropy mode. Both problems, fast and slow are then analyzed. The flame motion forces inlet duct acoustics. A numerical simulation of the flame motion shows that for typical combustor dimensions, the flame will eventually reach the exhaust nozzle, thus not only forcing inlet acoustics, but also creating conditions for the bulk instability. However, assuming the slow problem to remain stable, once the flame reaches the nozzle, its motion approaches a stable, stationary pattern. This validates the assumption that the long time scale, bulk oscillation is the instability mechanism. Results of a stability analysis for the slow problem show the bulk/entropy mode to be unstable if the burning rate decreases at a sufficiently strong rate when the velocity at the inlet to the combustor increases.