A method of adding or removing a gas to or from a solution of the gas in a liquid involves transferring the gas between the liquid and another fluid through a membrane unit. The membrane unit includes a membrane which is (i) substantially impermeable to the solvent and having a permeability to oxygen of at least 100 barrers; (ii) formed from an amorphous copolymer of perfluoro-2,2-dimethyl-1,3-dioxole; and (iii) is maintained at a temperature below the glass transition temperature of the copolymer. The fluid can be another liquid or a gas. The novel method provides very high rates of gas transmission between liquids and permits gasifying liquids without resort to sparging bubbles through the liquid. The method thus can gasify liquid with superior efficiency and without excessive agitation due to bubbling. These features result in economy of gas consumption and reduced need for gas recovery equipment, and when used in connection with a toxic or organic gaseous component, reduced requirements for additional pollution control equipment. The membrane material is resistant to fouling by liquids, and especially, by bioreactor mass. Hence, the novel method can remain in service for long duration without substantially diminished performance. Utilities for the novel method include purifying drinking water through ozonolysis, oxygenating bioreactors and blood; oxidizing volatile organic compounds in water; adding gaseous reactants to liquid chemical reactions and supplying oxygen to and removing volatile pollutants from waste water.