Process for purifying or separating a gas or gas mixture using a monolithic adsorbent for the separation or purification of gases or gas mixtures, having a cellular structure with open porosity in the form of a solid foam permeable to the gas molecules. The gas phase of the adsorbent possesses an essentially convex structure and the solid phase an essentially concave structure. The solid foam has a density of greater than or equal to 500 kg/m.sup.3 and an open porosity of between 20 and 60%. The gas is air or an H.sub.2/CO mixture. The process is of the VSA, PSA or TSA type. This process can be used in particular in OBOGS-type systems to supply passengers of the vehicle or a device participating in the traction of the vehicle and/or in its electrical supply, in particular a fuel cell. This process can also be used in medical oxygen concentrators.