We calculate the fate of postulated near surface brines on Mars. No stable brine system can exist on Mars today. The integrated H2O flux from a subsurface H2O reservoir is greater than zero at all latitudes where the highest recurring temperature exceeds the eutectic of chemically reasonable brines. Nonequilibrium brine systems or brine systems in dynamic equilibrium are possible. We calculate the rate of H2O mass loss from subsurface brines as a function of latitude, depth, regolith porosity, eutectic temperature, and pore size. Some brines may exist in the near-equatorial subsurface of Mars for periods on the order of 107 years. Seasonally variable radar reflectivity of the Martian surface has been interpreted as indicative of melting of subsurface brines (Zisk and Mouginis-Mark 1980). We present a model for a chemically reasonable brine that could reproduce radar results and estimate the escape rate of H2O molecules from such a brine. The presence of a low-permeability duricrust may be required to preserve such a brine for reasonable periods and to prevent detection of an areally extensive subsurface system by the Viking MAWD instrument. A porosity no lower than 20-30% should suffice to reduce H2O escape fluxes to the required rates.