Abstract: A method and a plant for producing liquid CO2 out of combustion flue gases wherein the flue gas is partially condensed in a single stage phase separation, the single stage phase separation comprising at least one heat exchanger (11, 17) and a separation drum (19), wherein the at least one heat exchanger (11, 17) is cooled by expanded offgas (23) and expanded liquid CO2 (3.3) and wherein a first part of the expanded CO2 (3.3) is separated after having passed the at least one heat exchanger (17) into liquid CO2 and gaseous CO2 in an additional separation drum (33), wherein the gaseous CO2 (3.4) and the liquid CO2 (3.5) of the additional separation drum (33) are expanded to a first pressure level (flag 7d?) wherein a second part of the liquid CO2 (3.6) of the separation drum (33) is expanded to a second pressure level (flag 7e?) for cooling the flue gas in the at least one heat exchanger (17).