In order to remove the olefinic impurities (in particular 1-chloro-2,2-difluoroethylene and polyfluoropropenes) present in crude 1,1,1,2-tetrafluoroethane (F134a), a gaseous mixture of crude F134a, hydrofluoric acid and oxygen or air is treated in the gas phase, in the presence of a fluorination catalyst, at a temperature between 200.degree. and 350.degree. C. and at a pressure between atmospheric pressure and 2.5 MPa, the HF/F134a molar ratio being between 0.05 and 0.5 and the O.sub.2 /F134a molar ratio being between 0.001 and 0.1.