We derive a general analytical solution for one-dimensional steady state two-phase hydrothermal flow in porous media. The solution indicates that saturation jumps associated with discontinuities in material properties of porous media, such as permeability and thermal conductivity, and phase change boundaries are common in these systems. Using linear stability analysis, we then show that the saturation jump associated with discontinuities in permeability or thermal conductivity of porous media can be unstable under infinitesimal perturbation. We also provide a simple numerical example to show that saturation waves attributed to the instability can propagate away from the discontinuity as relatively undamped oscillations. Because rapid spatial changes in material properties are likely in nature, we suggest that two-phase hydrothermal systems may often exhibit oscillatory behavior. When observational data on oscillations become available, such data may yield information on permeability and/or thermal conductivity structures of two-phase hydrothermal systems. ¿ 1998 American Geophysical Union