A process and an installation for the production of a variable flow rate of at least,one principal constituent of air under pressure, wherein a constituent is withdrawn in liquid phase from an air distillation apparatus (12), this liquid is brought to a vaporization pressure, and the liquid is vaporized under this vaporization pressure by heat exchange (in 9) with a calorific fluid under high pressure. The flow rate of the constituent is adjusted by modifying the flow rate of the liquid to be vaporized and the vaporization pressure. The vaporization pressure is intermediate the withdrawal pressure and the production pressure. The gas resulting from the vaporization is compressed in a compressor (20) to the production pressure.