Air-separation method by cryogenic distillation in an installation comprising a double or triple air-separation column, wherein the column operating at the highest pressure operates at a so-called medium pressure, and an exchange line where all the air intended for distillation is cooled, in which, in normal operation: a) all the air is raised to a high pressure greater than the medium pressure by at least 5 bar and purified at this high pressure, b) the purified air is divided into two fractions (13, 15), c) a first fraction at high pressure is sent to a hot supercharger, the supercharged first fraction cools in the exchange line to an intermediate temperature, d) the cooled first fraction is divided into two portions (31, 33), each portion expands in a respective turbine (T1, T2), e) the inlet pressure of the first and second turbines is, or the pressures of the two turbines are, greater than the medium pressure by at least 5 bar, f) the discharge pressure of at least one of the two turbines is substantially equal to the medium pressure, g) at least part of the air expanded in at least one of the turbines is sent to the medium-pressure column of the double or triple column, h) a second fraction of the purified air at high pressure is cooled in a first series of passages of the exchange line and next supercharged with an inlet temperature equal to an intermediate temperature of the exchange line in a cold supercharger mechanically connected to the second turbine, the hot supercharger being mechanically connected to the first turbine, i) the cold supercharger discharges the second fraction of air at a temperature higher than the inlet temperature, and the second fraction of air thus supercharged is reintroduced into a second series of passages of the exchange line, optionally at an intermediate point thereof, wherein at least some of the second fraction condenses or pseudocondenses, j) at least one pressurised liquid coming from one of the columns of the double or triple column is vaporised or pseudovaporised in the exchange line at a vaporisation temperature and characterised in that if, optionally only if, the cold supercharger is not functioning, the pressurised liquid coming from one of the columns of the double or triple column is vaporised or pseudovaporised in the exchange line and a first part of the purified air at high pressure is sent to the hot supercharger, cools in the first series of passages of the exchange line, emerges from the exchange line without passing through the cold supercharger and enters the exchange line in the second series of passages, the air that has passed through these two series of passages liquefies and is sent to at least one column of the double or triple column. a) all the air is raised to a high pressure greater than the medium pressure by at least 5 bar and purified at this high pressure, b) the purified air is divided into two fractions (13, 15), c) a first fraction at high pressure is sent to a hot supercharger, the supercharged first fraction cools in the exchange line to an intermediate temperature, d) the cooled first fraction is divided into two portions (31, 33), each portion expands in a respective turbine (T1, T2), e) the inlet pressure of the first and second turbines is, or the pressures of the two turbines are, greater than the medium pressure by at least 5 bar, f) the discharge pressure of at least one of the two turbines is substantially equal to the medium pressure, g) at least part of the air expanded in at least one of the turbines is sent to the medium-pressure column of the double or triple column, h) a second fraction of the purified air at high pressure is cooled in a first series of passages of the exchange line and next supercharged with an inlet temperature equal to an intermediate temperature of the exchange line in a cold supercharger mechanically connected to the second turbine, the hot supercharger being mechanically connected to the first turbine, i) the cold supercharger discharges the second fraction of air at a temperature higher than the inlet temperature, and the second fraction of air thus supercharged is reintroduced into a second series of passages of the exchange line, optionally at an intermediate point thereof, wherein at least some of the second fraction condenses or pseudocondenses, j) at least one pressurised liquid coming from one of the columns of the double or triple column is vaporised or pseudovaporised in the exchange line at a vaporisation temperature and characterised in that if, optionally only if, the cold supercharger is not functioning, the pressurised liquid coming from one of the columns of the double or triple column is vaporised or pseudovaporised in the exchange line and a first part of the purified air at high pressure is sent to the hot supercharger, cools in the first series of passages of the exchange line, emerges from the exchange line without passing through the cold supercharger and enters the exchange line in the second series of passages, the air that has passed through these two series of passages liquefies and is sent to at least one column of the double or triple column.