A computational scheme was developed for the transient combustion of premixed propane and air inside an adiabatic refractory tube. To test this scheme, steady-state solutions were obtained to provide initial and final conditions for the transient combustion. Multiple steady-state solutions were found to exist for some combinations of the mass how rate and the waif temperature at the inlet for a specified fuel-air ratio. Since complete transient computations that included the tube-wall temperature took an excessive amount of time, illustrative computations were carried out to completion only for a fixed tube-wall temperature that had previously been computed from a steady-state model. The-se transient computations for such a fixed tube-wall temperature provide a good approximation for the general behavior for short times owing to the great thermal inertia of the wall. The flame front moved very quickly toward the new location not only from an upstream location to a downstream one, but also from a downstream location to an upstream one. The movement of the dame front to a new location after heating the tube wall for a short time was also successfully computed. These results suggest that the wall temperature profile is the primary determinant of the stability of the flame in a refractory tube.