Process for the separation of air by cryogenic distillation in which i) air is compressed in a compressor having at least two stages (C1,C2) to form compressed air, all of the air compressed in the first of the two stages being compressed in the second of the two stages, ii) compressed air compressed in the second stage of the compressor is purified in a first adsorption vessel of a purification unit, having at least first and second adsorption vessels connected in parallel, to form purified air, iii) purified air from the purification unit is cooled from an ambient temperature to a cryogenic temperature in a heat exchanger and separated in a distillation column system to produce a fluid enriched in oxygen and/or a fluid enriched in nitrogen iv) a gas enriched in nitrogen is removed from the distillation column system, v) the gas enriched in nitrogen is warmed upstream of the second adsorption vessel by indirect heat exchange with air to cool the air, the air having been compressed in the first stage of the compressor and to be compressed in the second stage of the compressor, vi) the warmed gas enriched in nitrogen is sent to the second adsorption vessel as a regeneration gas, without being expanded in a turbine characterized in that the gas enriched in nitrogen is warmed to a temperature of at least 90°C upstream of the second adsorption vessel, the gas enriched in nitrogen being warmed by heat exchange with air by means of a closed circuit (17,P) in which water circulates at a pressure higher than 1.5 bars abs., preferably at a pressure higher than 5 bars abs, and a further stream of gas enriched in nitrogen removed from the distillation column is warmed by another means, for example an electrical heater, to form a further warmed stream, the further warmed stream being hotter than the gas enriched in nitrogen warmed to a temperature of at least 90°C and the further warmed stream being sent after mixing with the gas enriched in nitrogen warmed to a temperature of at least 90°C to the second adsorption vessel. i) air is compressed in a compressor having at least two stages (C1,C2) to form compressed air, all of the air compressed in the first of the two stages being compressed in the second of the two stages, ii) compressed air compressed in the second stage of the compressor is purified in a first adsorption vessel of a purification unit, having at least first and second adsorption vessels connected in parallel, to form purified air, iii) purified air from the purification unit is cooled from an ambient temperature to a cryogenic temperature in a heat exchanger and separated in a distillation column system to produce a fluid enriched in oxygen and/or a fluid enriched in nitrogen iv) a gas enriched in nitrogen is removed from the distillation column system, v) the gas enriched in nitrogen is warmed upstream of the second adsorption vessel by indirect heat exchange with air to cool the air, the air having been compressed in the first stage of the compressor and to be compressed in the second stage of the compressor, vi) the warmed gas enriched in nitrogen is sent to the second adsorption vessel as a regeneration gas, without being expanded in a turbine characterized in that the gas enriched in nitrogen is warmed to a temperature of at least 90°C upstream of the second adsorption vessel, the gas enriched in nitrogen being warmed by heat exchange with air by means of a closed circuit (17,P) in which water circulates at a pressure higher than 1.5 bars abs., preferably at a pressure higher than 5 bars abs, and a further stream of gas enriched in nitrogen removed from the distillation column is warmed by another means, for example an electrical heater, to form a further warmed stream, the further warmed stream being hotter than the gas enriched in nitrogen warmed to a temperature of at least 90°C and the further warmed stream being sent after mixing with the gas enriched in nitrogen warmed to a temperature of at least 90°C to the second adsorption vessel.