Abstract. A model problem for the propagation of a combustion front through a periodically inhomogeneous medium is posed. The existence of a steady state solution is proved, in which the front's velocity is periodic in time. Computer simulations are carried out. Finally, through rigorous homogenization techniques, it is shown that when the wavelength of the inhomogeneity is small, the solution may be approximated by a travelling wave solution of the corresponding problem for a medium with certain constant properties.