A method for purifying, by gas-liquid absorption, an incoming gas flow comprising a gas G 0 to be purified and at least one acid gas Ga 1 to be removed, said gas G 0 to be purified having a Henry's law H G0 less than 10 -2 mol.L -1.bar -1 and said acid gas Ga 1 to be removed having a Henry's law H Ga1 greater than 10 -2 mol.L -1.bar -1 and an acid dissociation constant pKa Ga1 greater than or equal to 1 and less than or equal to 13, said method comprising at least the following steps: - during an absorption step, through an absorption membrane unit comprising at least one gas-permeable and hydrophobic membrane, said incoming gas flow on one side of said membrane is brought into contact with an aqueous solvent, capable of absorbing the soluble gases and circulating on the other side of said membrane, and a rich aqueous solvent comprising said acid gas Ga 1 dissolved and an exiting gas flow enriched with gas G 0 to be purified are obtained, said solvent comprising at least one aqueous solution comprising water and at least one salt selected from NaCl, KCI, Na 2 SO 4, K 2 SO 4, NaNOs, KNOs NaBr, KBr, Nal, KI, LiCI, LiBr, Lil, Li 2 SO 4 LiNO 3, the molar concentration of salt in the absorbent liquid is between 0.2 and 6 mol.L -1; - during a desorption step, said rich aqueous solvent is brought into contact with a desorption membrane unit comprising at least one membrane that is permeable to gases and hydrophobic, and, by applying a transmembrane negative pressure, said dissolved acid gas Ga 1 is removed from said rich aqueous solvent which circulates on one side of said membrane, by passing through said membrane toward the other side thereof, in order to obtain a degassed aqueous solvent; - said degassed aqueous solvent is recycled in the absorption step, all of the steps of said method being continuously operated in a closed loop, said aqueous solvent (3, 30, 31) being circulated in a closed-loop circuit between said absorption membrane unit and said desorption membrane unit; said method being characterized in that: - the pH of the aqueous solvent (3, 31) is adjusted to a value greater than or equal to pKa Ga1 +2 and less than or equal to 13, by adding a basic solution, before the absorption step, and the pH of the rich aqueous solvent is adjusted to a value greater than or equal to pKa Ga1 -2 and less than or equal to pKa Ga1 +1, by adding an acid solution, before the desorption step, said aqueous solvent having a buffer agent concentration of less than 0.02 mol.L -1; and in that the base and the acid are regenerated from the degassed aqueous solvent, added to said aqueous solvent (3, 30, 30', 31) to adjust the pH, by a step of bipolar membrane electrodialysis. - during an absorption step, through an absorption membrane unit comprising at least one gas-permeable and hydrophobic membrane, said incoming gas flow on one side of said membrane is brought into contact with an aqueous solvent, capable of absorbing the soluble gases and circulating on the other side of said membrane, and a rich aqueous solvent comprising said acid gas Ga 1 dissolved and an exiting gas flow enriched with gas G 0 to be purified are obtained, said solvent comprising at least one aqueous solution comprising water and at least one salt selected from NaCl, KCI, Na 2 SO 4, K 2 SO 4, NaNOs, KNOs NaBr, KBr, Nal, KI, LiCI, LiBr, Lil, Li 2 SO 4 LiNO 3, the molar concentration of salt in the absorbent liquid is between 0.2 and 6 mol.L -1; - during a desorption step, said rich aqueous solvent is brought into contact with a desorption membrane unit comprising at least one membrane that is permeable to gases and hydrophobic, and, by applying a transmembrane negative pressure, said dissolved acid gas Ga 1 is removed from said rich aqueous solvent which circulates on one side of said membrane, by passing through said membrane toward the other side thereof, in order to obtain a degassed aqueous solvent; - said degassed aqueous solvent is recycled in the absorption step, all of the steps of said method being continuously operated in a closed loop, said aqueous solvent (3, 30, 31) being circulated in a closed-loop circuit between said absorption membrane unit and said desorption membrane unit; - the pH of the aqueous solvent (3, 31) is adjusted to a value greater than or equal to pKa Ga1 +2 and less than or equal to 13, by adding a basic solution, before the absorption step, and the pH of the rich aqueous solvent is adjusted to a value greater than or equal to pKa Ga1 -2 and less than or equal to pKa Ga1 +1, by adding an acid solution, before the desorption step, said aqueous solvent having a buffer agent concentration of less than 0.02 mol.L -1;