A process for separating air by cryogenic distillation in a column system comprising a high pressure column (8) and a low pressure column (9) comprises the steps of: compressing all the feed air in a first compressor (6) to a first outlet pressure at most two bars higher than the pressure of the high pressure column, sending a first part of the air at the first outlet pressure to a second compressor (230) and compressing the air to a second outlet pressure, cooling and condensing at least part of the air at the second outlet pressure in a heat exchanger (5), removing liquid from a column of the column system, pressurizing the liquid and vaporizing the liquid by heat exchange in the heat exchanger and at least partially vaporizing an auxiliary fluid in the heat exchanger, possibly further warming said auxiliary fluid in the heat exchanger, sending at least part of this auxiliary fluid to a third compressor (108) to be compressed to a third outlet pressure, introducing at least part of said auxiliary fluid at said third outlet pressure in the heat exchanger, wherein the inlet of the third compressor is at a subambient temperature.