Air is fractionated in a double distillation column 4 comprising lower pressure and higher pressure columns 8 and 6 respectively. Condenser-reboiler 42 provides reboiled oxygen to the bottom of the column 8. Liquid nitrogen reflux is introduced into the top of the column 8 through an inlet 50. Oxygen, nitrogen and argon-enriched streams are withdrawn from the column 8 through outlets 52, 54 and 58 respectively. The argon-enriched stream is separated in a further distillation column 40 and a product argon stream is withdrawn through outlet 62. A liquid stream is withdrawn through outlet 70 from an intermediate level of the column 8 is at least partially reboiled in heat exchanger 72, and is returned to the column 8 through inlet 74 at a level where the composition of the vapour corresponds approximately to that of the reboiled liquid. Heating for the heat exchanger 72 is provided by a vapour stream withdrawn through outlet 76 from the column 40, which vapour stream condenses and is returned to the column 40 through inlet 75. The aforesaid reboiling of the stream from the intermediate level of the column 8 makes possible more efficient air separation.