We investigate the nonthermal escape of oxygen from Mars due to the dissociative recombination of O₂ ⁺. By combining a time-dependent two-stream model for the nonthermal oxygen with an MHD model of the ionosphere-magnetosheath interaction, the response of the oxygen escape rate to time-varying solar wind conditions is examined. Over the last few decades a number of model calculations of expected nonthermal oxygen escape have been performed, but all assumed steady state conditions. In this study we calculate the time variation of the nonthermal escape rate after enhancement of the solar wind dynamic pressure. We find that the escape rate of nonthermal oxygen increases by a factor of about two to four as the ionosphere is compressed in response to solar wind dynamic pressure enhancement. We also find that in steady states the escape rate for high ionopause altitude cases (h ∼ 600 km) is twice as large as that for low ionopause altitude cases (h ∼ 250 km) due to non-negligible dissociative recombination above the exobase.