The evolution of the Mars atmosphere, with regard to water, is influenced by non-thermal escape of oxygen atoms. In our evaluation of the various escape processes we recognized that the widely quoted escape rates for oxygen atoms originating from dissociative recombination (exospheric O) are too high by an order of magnitude. Thus the originally postulated coupling of H and O escape in the ratio of 2:1 can no longer be maintained. This has important implications for the stability of the Martian CO2 atmosphere. This study takes into account temperature dependent photodissociation coefficients, optical depths, ozone chemistry, hydrogen and oxygen escape fluxes for conditions of an ancient dense Mars atmosphere. Since the only source of hydrogen is water, the calculated hydrogen escape flux represents an upper limit for an equivalent water loss to space. Under this constraint, we find much lower oxygen escape rates originating from water than current estimates, implying a loss of H2O to space corresponding to an equivalent depth ≤5 meter over the last 3.5 billion years. Our results cast serious doubt on previous estimates that as much as 50--80 meters of H2O were lost to space during this period. ¿ American Geophysical Union 1996