Abstract: The invention relates to a method to reduce flue gas in incineration processes that are carried out with an oxidizing incineration gas consisting of a flue gas that is returned to the circulation system and of a technically produced oxygen. A stoichiometrically-related proportion of the flue gas that is not added to the incineration gas has a CO.sub.2 fraction greater than 70%. In order to reduce the flue gas, the fraction of flue gas that is returned and not used as incineration gas in the incineration process is removed from the circulation system and liquefied in the device.