Thermodynamic analysis of the system CO2-H2O shows that although CO2 clathrate and liquid CO2 are stable over most of the pressure and temperature range expected for the Martian regolith, hydraulic equilibrium of the regolith pore gas with the overlying atmosphere, a condition most likely in equatorial regions, will destabilize both phases. Condensation on Mars comes in four predictable assemblages: pure H2O ice, CO2 clathrate (hydrate), a eutectic mixture of solid CO2 and either clathrate or H2O ice (if the clathrate fails to nucleate), and under limited conditions, pure solid CO2. Seasonal frosts are likely to consist of thin layers of water ice and/or clathrate, overlain by the eutectic assemblage. Growing ice caps are also likely to be layered, with sets of ice (lower) and eutectic (upper) layers interspersed with pure solid CO2 layers. The saturated water content of a 1-bar CO2 atmosphere with surface temperatures >273 K would have reached 20 precipitable millimeters. Basal melting, triggered by trapped heat flow from the interior, limits the thickness and composition of the polar ice caps and is to be expected during periods of low obliquity, when there is extensive cooling and condensation at the poles. Introduction of liquid CO2 into the Martian regolith by basal melting at the poles may be a major mechanism for loss of the ancient greenhouse atmosphere and its long-term sequestration. Explosive release of CO2 fluid coexisting with groundwater may trigger outflow channel floods and reset atmospheric isotope ratios.