The stability of water ice, epsomite, and hexahydrite to loss of H2O molecules to the atmosphere at equatorial latitudes of Mars was studied to determine their potential contributions to the measured abundance of water-equivalent hydrogen (WEH). Calculation of the relative humidity based on estimates of yearly averages of water-vapor pressures and temperatures at the Martian surface was used for this purpose. Water ice was found to be sufficiently unstable everywhere within 45¿ of the equator that if the observed WEH is due to water ice, it requires a low-permeability cover layer near the surface to isolate the water ice below from the atmosphere above. In contrast, epsomite or hexahydrite may be stable in many near-equatorial locations where significant amounts of WEH are observed.