We study the linear stability of a two-phase heat pipe zone (vapor-liquid counterflow) in a porous medium, either overlying a superheated vapor zone or underlying a subcooled liquid zone. The effects of gravity, condensation and heat transfer on the stability of a planar base state are analyzed in the linear stability limit. The rate of growth of unstable disturbances is expressed in terms of the wave number of the disturbance, and dimensionless numbers, such as the Rayleigh number and a dimensionless heat flux. As in natural convection under single-phase conditions, a critical Rayleigh number exists, above which the system is conditionally unstable. The critical number takes values different than under single-phase conditions and also depends on the applied heat flux. The results find applications to geothermal systems, to enhanced oil recovery using steam injection, as well as to the conditions of the proposed Yucca Mountain nuclear waste repository. This study complements work of the stability of boiling by Ramesh and Torrance [J. Fluid Mech. 257 (1993) 289]. (C) 2003 Elsevier Ltd. All rights reserved.