A method for bringing into contact two phases which are not completely miscible with one another, and whose contact is accompanied by heat development owing to mass transfer and/or chemical reaction, in which a first phase is introduced into the lower region of a contactor and a second phase is introduced into the upper region of the contactor and passed in countercurrent flow to the first phase in the contactor, a treated first phase and an exhausted second phase being obtained, which comprises recirculating a part of the exhausted second phase to the contactor at least one point situated between the upper region and the lower region. In the preferred embodiment, the first phase is a fluid stream comprising acid gases such as CO2, H2S, SO2, CS2, HCN, COS or mercaptans, and the second phase is an absorption medium which comprises an aqueous solution of at least one organic and/or inorganic base.