In Part II of this paper the analysis is extended to include both conduction and non-zero net mass flow. We are able to distinguish between low and high enthalpy two-phase reservoirs, where the former must terminate in single-phase liquid conditions at depth, while the latter may end in single-phase liquid (for low permeabilities), single-phase vapour (for intermediate permeabilities), or can be unstable when extended (for high permeabilities). If, and only if, both conduction and net mass Row are non-zero a class of models can be identified with the property that a permeability increase (downwards) is associated with a liquid saturation decrease. This provides a prototype for a vapour-dominated geothermal reservoir.