Contrary to tropospheric CO<sub>2</sub> whose oxygen isotopic composition follows a standard mass dependent relationship, i.e. δ<sup>17</sup>O~0.5δ<sup>18</sup>O, stratospheric CO<sub>2</sub> is preferentially enriched in <sup>17</sup>O, leading to a strikingly different relation: δ<sup>17</sup>O~1.7δ<sup>18</sup>O. It has been shown repeatedly that the isotope anomaly is inherited from O<sub>3</sub> via photolytically produced O(<sup>1</sup>D) that undergoes isotope exchange with CO<sub>2</sub> and the anomaly may well serve as a tracer of stratospheric chemistry if details of the exchange mechanism are understood. We have studied the photochemical isotope equilibrium in UV-irradiated O<sub>2</sub>-CO<sub>2</sub> and O<sub>3</sub>-CO<sub>2</sub> mixtures to quantify the transfer of the anomaly from O<sub>3</sub> to CO<sub>2</sub> at room temperature. By following the time evolution of the oxygen isotopic compositions of CO<sub>2</sub> and O<sub>2</sub> under varying initial isotopic compositions of both, O<sub>2</sub>/O<sub>3</sub> and CO<sub>2</sub>, the isotope equilibria between the two reservoirs were determined. A very strong dependence of the isotope equilibrium on the O<sub>2</sub>/CO<sub>2</sub>-ratio was established. Equilibrium enrichments of <sup>17</sup>O and <sup>18</sup>O in CO<sub>2</sub> relative to O<sub>2</sub> diminish with increasing CO<sub>2</sub> content, and this reduction in the equilibrium enrichments does not follow a standard mass dependent relation. When molecular oxygen exceeds the amount of CO<sub>2</sub> by a factor of about 20, <sup>17</sup>O and <sup>18</sup>O in equilibrated CO<sub>2</sub> are enriched by (142±4)‰ and (146±4)‰, respectively, at room temperature and at a pressure of 225 hPa, independent of the initial isotopic compositions of CO<sub>2</sub> and O<sub>2</sub> or O<sub>3</sub>. From these findings we derive a simple and general relation between the starting isotopic compositions and amounts of O<sub>2</sub> and CO<sub>2</sub> and the observed slope in a three oxygen isotope diagram. Predictions from this relation are compared with published laboratory and atmospheric data.