Process for the production of oxygen by cryogenic distillation of a supply mixture containing oxygen and nitrogen in a double column (5) comprising a medium pressure column (6) and a low pressure column (7), in which there is partially condensed at least one fraction of the supply mixture in a condenser (8) by vaporization of liquid oxygen from the base of the low pressure column (7), said partially condensed mixture is sent to the medium pressure column (6), all the oxygen destined to form the gaseous production being withdrawn in liquid phase from the base of the low pressure column (7), and brought to its utilization pressure.