It has been concluded from measurements, recently made by Mars Odyssey experiments, that there is water in the upper few metres of the Martian surface at mid- and equatorial latitudes with regionally high contents of up to about 9 wt%. This Martian subsurface water is shown to be in the form of adsorption (or sorption) water. The adsorptive bond of water molecules is about twice as strong on mineral surfaces compared with on water ice. Therefore, evaporation of adsorption water in porous soil happens on time scales, which exceed those of sublimation of water ice by orders of magnitude. Consequently, sorption water can have survived in the near-surface layers of the Martian soil at mid- and equatorial latitudes over geological time scales, where ice must have been lost by sublimation. Sorption water is unfrozen, i.e. liquid-like, down to temperatures of −40°C and below. It must, at least regionally and temporarily, be an important and not a trace constituent of the upper-surface Martian soil. The presence of liquid-like sorption water on Mars is also discussed in view of exobiological implications.