According to a first step in an air separation unit, all the air intended for distillation is compressed in a main compressor (1), a first stream of air, compressed in at least the main compressor, purified and cooled in a heat exchange line (6), is sent to the medium-pressure column (8) of a double column, said stream of air is divided into a nitrogen-enriched stream and an oxygen-enriched stream in the medium-pressure column, a liquid oxygen stream (16) is withdrawn from the low-pressure column, said stream is pressurized up to a high pressure and vaporized in the heat exchange line in order to form a first high-pressure oxygen-rich gas stream, at least one portion (24) of the air compressed in the main compressor is liquefied and the liquefied portion is sent to the double column, and a second oxygen-rich gas stream (115) is also produced, but at a lower pressure than the first oxygen-rich gas stream, and, in a second step, the air liquefaction pressure is increased by adjusting the blades of the main compressor (1), which set this pressure, the production of the second oxygen-rich gas stream is reduced, and the withdrawal of the first oxygen-rich gas stream is increased.