To better understand natural two-phase hydrothermal systems, we have constructed one-dimensional heat-pipe solutions for NaCl-H2O fluids and explored the effects of basal heat flux and permeability on their behavior. For seafloor conditions, saline brines form quickly at the base of the heat pipe; and in some cases halite is precipitated. NaCl-H2O heat pipes may become liquid or vapor dominated but, in contrast to their pure-water counterparts, often do not achieve steady state. When steady state solutions do exist, they are characterized either by broad, weak counter-flow or by vigorous counter-flow across a thin layer. The latter behavior may be analogous to that occurring in the Salton Sea Geothermal System, California.