Abstract: In a method of absorbing CO2 from a gas mixture the use of an absorption medium comprising water and at least one amine of formula (I) where R1 is a —(CH2)n—(XCH2CH2)m—Y—R3 radical where R3=hydrogen or an alkyl radical having from 1 to 6 carbon atoms, X and Y are each, independently of one another, NR3, oxygen, SO or SO2, where in the case of Y?SO and in the case of Y?SO2, R3 is not hydrogen, and Y—R3 can be an N-morpholinyl radical or an N-piperazyl radical, n=2 to 4, m=0 to 4 and R2 is hydrogen, an alkyl radical having from 1 to 6 carbon atoms or a radical R1, where m is not 0 when R2 is not a radical R1, Y?NR3 and Y—R3 is not an N-morpholinyl radical and not an N-piperazyl radical, makes it possible to avoid precipitation of a solid during the absorption of CO2 and a separation into two liquid phases during the regeneration of the absorption medium.