The absorptive removal of carbon dioxide from biogas using a scrubbing liquid in which carbon dioxide is chemically bound proceeds by heating the loaded scrubbing liquid, occurring after the absorption, to a temperature at which liberation of CO2 begins. Immediately thereafter, the loaded scrubbing liquid is fed to at least one centrifugal separator for separating off the gas phase from the liquid phase, wherein methane and dissolved fractions of CO2 escape via the gas phase. After separation is complete, the gas phase is passed into the absorber unit and the liquid phase is further heated to the temperature required for desorption and fed to the desorption unit for regeneration.