In an integral incorporated cascade-type process the cooling mixture from the penultimate stage (1B) of the single cycle compressor (1) is fed into a distillation apparatus (5), the overhead vapour of which is cooled (at 24) to a temperature considerably less than ambient temperature. The vapour is then separated into two phases (at 6C); the vapour phase supplies the last stage (1C) of the compressor, and the liquid phase provides a cooling fluid for the hot part (8) of the thermal exchange line (7).