NOVELTY - The process comprises cooling a liquid absorbent solution enriched in acidic compounds, contacting the feed gas with the liquid absorbent solution enriched in the acidic compounds in a first cocurrent contactor (C1), where the feed gas and the absorbent solution transverse, according to vertical and horizontal directions, the first contactor from an inlet to an outlet to produce gas depleted in the acidic compounds and the absorbent solution responsible in the acidic compounds, and contacting the gas depleted in acidic compounds with liquid absorbent solution in a second cocurrent contactor.    USE - The process is useful for the deacidification of a feed gas comprising acidic compounds including carbon dioxide and hydrogen sulfide, where the feed gas consists of a combustion flue, a natural gas, a tail gas from the Claus process, a synthesis gas, a gas from a fermentation biomass, an effluent from a cement and a gas from a steel and iron industry (claimed).    ADVANTAGE - The method ensures effective and economic deacidification of the feed gas without pollution.    DETAILED DESCRIPTION - The process comprises cooling a liquid absorbent solution enriched in acidic compounds, contacting the feed gas with the liquid absorbent solution enriched in the acidic compounds in a first cocurrent contactor (C1), where the feed gas and the absorbent solution transverse, according to vertical and horizontal directions, the first contactor from an inlet to an outlet to produce gas depleted in the acidic compounds and the absorbent solution responsible in the acidic compounds, contacting the gas depleted in acidic compounds with the liquid absorbent solution in a second cocurrent contactor (C2), where the gas and the absorbent solution transverse, according to the vertical and horizontal directions, the second cocurrent contactor from the inlet to the outlet to produce a lean gas in acidic compounds and the liquid absorbent solution, and contacting the gas depleted in acidic compounds with a liquid absorbent in a third cocurrent contactor (C3), where the gas and the liquid absorbent solution transverse, according to the vertical and horizontal directions, the third contactor from the inlet to the outlet to produce treated gas and the liquid absorbent solution. The contactors comprise a liner having a geometric area of greater than 400 m2/m3. The method further comprises circulating the gas in the contactors at a speed of greater than 2 m/s and 4 m/s, removing a portion of gas and the liquid absorbent solution from the outlet of one of the contactors, increasing the pressure of the portion of gas and the liquid absorbent solution, introducing the gas and the liquid absorbent solution at the inlet of the contactor, and regenerating the absorbent solution loaded with the acidic compounds so as to release the acidic compounds and to produce the absorbent solution or liquid absorbent.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of three vertical columns.    Conduits (1, 2, 3, 4, 5, 6, 7, 8, 9)    First cocurrent contactors (C1)    Second cocurrent contactors (C2)    Third cocurrent contactors (C3)    Heat exchangers. (E1, E2)