We examine the stability of a vaporizing liquid front migrating through a permeable rock. We show that such liquid-vapor fronts may become unstable if a sufficient fraction of the liquid vaporizes. This instability is a result of the different speed of the fluid on each side of the front. We also identify that short-wavelength perturbations are stabilized by thermal conduction, while long-wavelength perturbations are stabilized as a result of the compressibility of the vapor. Furthermore, under conditions typical of geothermal reservoirs, where the pressure is ~10 atm and the temperature is ~200¿--300 ¿C, we find that if the permeability of the system is smaller than ~10-15 m2, then these two stabilizing mechanisms overlap and the system becomes stable to perturbations of any wavelength. We also examine the role of gravity in suppressing the instability of an ascending front and promoting the instability of a descending front. We apply our results to the vapor-dominated geothermal reservoirs at Larderello, Italy, and the Geysers, California, to predict conditions under which liquid fronts, advancing into superheated vapor, are stable. ¿ 1998 American Geophysical Union