In this process for purifying a gas by adsorption of a first impurity and of a second impurity, at least two main adsorbers (5A, 5B) and at least one auxiliary adsorber (6A, 6B) are used, the main adsorbers comprising a packing (8A, 8B, 9A, 9B) for adsorbing the first and second impurities. During at least a first step, the gas is purified by adsorbing the two impurities by passing through at least a first (5A, 5B) of the main adsorbers without passing through a first auxiliary adsorbers (6A, 6B), and simultaneously the second main adsorber (5A, 5B) and the or each auxiliary adsorbers (6A, 6B, 6) is regenerated in parallel, then, during a second step, at least some of the gas flow is purified by adsorption of the two impurities by passing in series through the first main adsorber (5A, 5B) and through the first auxiliary adsorber (6A, 6B). Application, for example, to the purification of air for the purpose of its distillation.