A linear stability analysis of vapour–liquid counter flow in porous media is carried out. For the vapour-dominated basic state the development in time of both pressure and saturation disturbances is studied. The pressure field is shown to be asymptotically stable for all choices of thermal boundary conditions, excluding the insulating–insulating boundary condition for which it is neutrally stable. The saturation field is proven to be Lyapunov stable: the saturation disturbance remains bounded by an infinitesimal number at all times. For both vapour- and liquid-dominated basic states the direction of propagation of small saturation disturbances is determined. These results explain the formation of two-layer geothermal structures and why alternative structures cannot develop within homogeneous reservoirs.