A process for the cryogenic separation of mixtures containing oxygen to obtain a produce having a high concentration of oxygen. In this process, a heat and material exchange occurs in counter-current between a descending liquid and a rising gas in at least one transfer zone including a bundle of organized linings consisting of cross-undulated metallic layers. In at least one transfer zone where the concentration of oxygen is higher than 98%, the layers are made of a sheet of aluminum having a thickness between 0.3 and 1 mm. Additionally, the bundles of layers have a specific surface lower than 400 m.sup.2 /m.sup.3.