A one-dimensional model of a counterflowing steam-water mixture above quiescent water in a porous medium is developed to study two-phase flow processes in vapor-dominated geothermal systems. Only if the temperature gradient in the underlying water lies between specified limits is it possible for a counterflowing steam-water mixture to overlie the water. In general, there is an abrupt jump in the steam fraction and the temperature gradient at the interface between the two-phase region depend on the magnitude of the temperature gradient in the water I' the temperature at the interface between the water and the steam-water mixture Td, and the permeability to thermal conductivity radio Kk; these dependences are studied quantitatively. For small K/k, the thickness of the two-phase region is essentially independent of K/k, whereas for large K/k the thickness of the region increases dramatically with K/k. For fixed K/k and I'. Normally, condensation of rising steam occurs in the two-phase region resulting in a steam flow which decreases with proximity to the surface and a water flow which increases with depth. However, downward flowing water can boil and add steam to the upflow.