The conditions for the onset of convection and the characteristics of the convection at the onset of instability are determined for a porous medium containing either a saturated liquid or a steam-water mixture. Convection is driven by a phase change instability mechanism. If steam and water are always in thermodynamic equilibrium, then temperature perturbations are directly responsible for pressure variations, which tend to move the fluid against the frictional resistance of the medium to flow. Mass conservation insures that any horizontal divergence of fluid is balanced by an appropriate vertical motion, while condensation and boiling occur to achieve a balance of forces in the vertical. Convection occurs more readily in a porous medium containing saturated liquid by the phase change instability than it would in a porous layer filled with ordinary water by the Rayleigh-B¿nard buoyancy-driven instability. Porous layers with steam-water mixtures are also more susceptible to convection than are those containing ordinary water. Phase-change-driven convection is concentrated toward the bottom of the porous layer; the cells are narrow in comparison to their depth.