A method is provided for producing carbon dioxide by combusting a carbonaceous fuel with oxygen or with a gas mixture containing more than 25 mol % of oxygen obtaining a flue gas mixture, wherein the flue gas mixture is processed obtaining a secondary gas mixture containing carbon dioxide and oxygen, and wherein a part of the oxygen contained in the secondary gas mixture is catalytically reacted with a first auxiliary fuel in a reactor system comprising a series of multiple reactors, obtaining further carbon dioxide and water. A further part of the oxygen contained in the secondary gas mixture is catalytically reacted with a second auxiliary fuel in the reactor system. A corresponding apparatus is also described herein.