An ozone-oxygen gas stream produced by passing oxygen into an ozone generator is introduced into a membrane separation unit containing an ozone-permeable membrane. Ozone-enriched gas passes through the membrane and is recovered or it contacts a liquid or gas stream which contains ozone-reactive substances, thereby oxidizing the substances. The oxygen-enriched gas stream produced on the feed side of the membrane by permeation of ozone through the membrane is recycled to the ozone generator. Prior to being recycled, the oxygen-enriched stream may be purified to remove gaseous impurities which permeate through the membrane from the liquid or gas stream being treated.