Mars has permanent water ice caps at both poles, which are seasonally covered by carbon dioxide ice.
What knowledge do we have regarding the age of the oldest ice in those caps?
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There are no direct measurements of this, but the caps are probably only a few million years old. All we have are estimated cratering ages, which indicate the surfaces of the polar caps are very young, and model estimates, which place special emphasis on a transition in the axis tilt behavior about 5 Myr ago.
According to this paper by Laboratoire de Météorologie Dynamique, IPSL, CNRS, Université Paris,
Mars undergoes cycles of colder and warmer climate, as the orbital obliquity cycles over a period of roughly 120 000 years.
The south polar regions appear to consist of multiple layers of alternate lighter and darker material, the result of accumulations during these cyclic variations.
Thus there is both CO2 ice and H2O ice on the south pole that has persisted largely intact through "multiple" cycles of 120 000 years each.
The north pole does not survive through a warm summer during a warmer period within the cycle though.
There may also be large areas of dust-covered permafrost at lower latitudes, which are a remnant of the previous cycle (thus "only" somewhat less than 120 000 years old)
Finally, there is some evidence that "it is likely that the large pore
volume of the Martian subsurface regolith might be partly filled by ice"
This would be ice remaining from when the average subsurface temperature of Mars first went below freezing, and can thus be up to some billions of years old.
So in summary: