Mars undergoes significant oscillations in its orbit, which will have a pronounced effect on its climate and, in particular, on the behavior of subsurface water ice. We explore and map the behavior of ice in the Martian near-surface regolith over the past 1 m.y. using a diffusion and condensation model presented in an earlier paper, with two primary modifications to include orbitally induced variations in insolation and atmospheric water abundance. We find that the past behavior of ground ice differs significantly from that at the present epoch, primarily the result of high-amplitude oscillations in obliquity (presently 25¿). In midlatitude and equatorial regions, ground ice will condense from atmospheric water during times of higher obliquity, filling the top few meters of the regolith with significant amounts of ice. At an obliquity of 32¿, ground ice becomes stable globally. During times of lower obliquity, ground ice will sublime and diffuse back into the atmosphere, dessicating the regolith to a depth of about 1 to 2 m equatorward of 60¿ to 70¿ latitude. In the high-latitude regions these oscillations are considerably subdued. Below this depth of cyclic saturation and dessication a long-term stability of ice exists in some geographic regions. We present a map of the distribution of ice expected at the present epoch. Cyclic exchange of water between the global regolith and polar regions will have significant implications for surface geology and the polar layered deposits. ¿ American Geophysical Union 1995