A process for the treatment of a gaseous mixture by adsorption with variable pressure, in an adsorption installation comprising at least one adsorber. For each adsorber, there is a succession of steps defining an adsorption phase, a regeneration phase for the adsorbent comprising a depressurization step, and a pressure increase phase. The passage from one phase to the following comprises switching of at least one valve between open and closed positions. At least one valve switching is carried out according to a programmed progressive slope to control a first cocurrent decompression stage of the adsorber with transfer of gas toward a lower pressure portion of the installation. The transferred gas is sent, for at least partially balancing pressure, to another adsorber in a pressure increase phase.