A method is described for separating CO2 and/or H2S from a mixed gas stream by contacting the gas stream with a non-aqueous, liquid absorbent medium of a primary and/or secondary aliphatic amine, preferably in a non-aqueous, polar, aprotic solvent under conditions sufficient for sorption of at least some of the CO2. The solution containing the absorbed CO2 can then be treated to desorb the acid gas. The method is usually operated as a continuous cyclic sorption-desorption process, with the sorption being carried out in a sorption zone where a circulating stream of the liquid absorbent contacts the gas stream to form a CO2-rich sorbed solution, which is then cycled to a regeneration zone for desorption of the CO2 (advantageously at 0.5:1 (approaching 1:1) may be achieved.