Process for selectively removing H.sub.2 S from a gas mixture including H.sub.2 S and CO.sub.2 comprising contacting the gas mixture in a first contacting zone (1) with lean absorbent to obtain loaded absorbent, heating in heat exchanger (15) loaded absorbent, flashing in separating vessel (5) the heated loaded absorbent to obtain a partly purified absorbent and a CO.sub.2 -rich gas mixture, contacting the CO.sub.2 -rich gas mixture with a lean absorbent in second contacting zone (7) to obtain H.sub.2 S-loaded absorbent, adding the H.sub.2 S-loaded absorbent to the loaded absorbent before heating, and regenerating the partly purified absorbent in a regenerating zone (9) to obtain lean absorbent and H.sub.2 S-rich gas.