Vapor-dominated geothermal systems similar to the Geysers in northern California and Kawah Komojang, West Java, are modeled as one-dimensional structures in a porous medium saturated with water and steam. The model consists of a near-surface condensate layer lying above a two-phase counter-flow region with rising steam and descending water. Real systems have condensate layers several hundred meters thick and vapor-dominated two-phase reservoir temperatures near 513 K. Models which reproduce these general characteristics have net mass flow rate M to thermal conductivity k ratios smaller than about 2.5¿10-7 m-3 and permeability K to thermal conductivity ratios larger than 4.5¿10-17 m s3 K kg-1. The mobil fluids in the main reservoirs of these models are essentially all steam. However, the reservoirs of real systems can contain substantial amounts of residual water. Temperature T and pressure p data in the main reservoir of the Kamajang system are best fit by models with K/k between 10115 and 10-14 m s3 K kg-1. Thus the permeability of the main reservoir is between 4¿10-15 and 4¿10-14 m2 (4 and 40 mdarcy) for k = 4 J m-1 K-1. These p and T data are not diagnostic of the overall flow rate through the Kamojang system. A relatively low permeability cap is required to stabilize the water layer above the steam region.