Abstract: Improvement in the enrichment of a gas in hydrogen sulphide, comprising selective absorption by a liquid in a primary absorption zone, regeneration of the liquid by heating and/or stripping by an inert gas with liberation of the gases absorbed and recovery of a fraction of the liberated gases, the remainder being subjected to a second absorption in a secondary absorption zone by a new or regenerated absorbent liquid identical with that used in the primary absorption zone; in one and the same zone of operation, common to the regeneration and the secondary absorption zones, there occur simultaneously: arrival of the liquid from the first absorption, movement of the gases liberated during regeneration, flow of the liquid derived from the secondary absorption and discharge of a fraction of the liberated gases enriched in H.sub.2 S.