The gaseous effluent to be treated is contacted in column C1 with an absorbent solution selected for its property of forming two separable phases when it is heated. The regenerated absorbent solution is separated into two phases in drum B1; a fraction rich in water and a fraction rich in reactive compounds.Separation allows to optimize the operations performed on the regenerated absorbent solution. On the one hand, separation allows to carry out vaporization, through reboiler R1, of a fraction of the absorbent solution, preferably containing a limited reactive compound concentration in relation to the absorbent solution, thus limiting their degradation. On the other hand, separation of the phases allows to reduce the amount of solution to be treated in order to remove the non-regeneratable salts and thus to reduce the costs linked with their elimination. Finally, separation allows to eliminate the degradation products by carrying out a specific and suitable purification for each phase.The method can be applied to combustion fumes decarbonation and to natural gas or synthesis gas deacidizing.