The present invention relates to a method of deacidizing a gaseous effluent comprising at least one of the acid compounds as follows: H2S, mercaptans, CO2, COS, SO2, CS2, wherein the following stages are carried out: a) contacting the acid compounds contained in said effluent with reactive compounds forming a liquid, so as to obtain a gaseous effluent depleted in acid compounds and a first liquid fraction comprising products formed by reaction of the reactive compounds with acid compounds, and reactive compounds that did not react with acid compounds, b) contacting said products contained in the first liquid fraction with extraction compounds forming a second liquid fraction so as to obtain a product-depleted first liquid fraction and a product-enriched second liquid fraction, c) recycling to stage a) the first liquid fraction obtained in stage b), said first liquid fraction obtained making up at least part of said liquid, d) regenerating the second liquid fraction obtained in stage b) so as to release acid compounds in gaseous form and to obtain a mixture of reactive compounds and of extraction compounds.