Abstract: The invention relates to a method for separating off and immobilizing carbon dioxide and/or carbon monoxide from an exhaust gas (18). In the method, a stoichiometric ratio of carbon dioxide to hydrogen, and/or of carbon monoxide to hydrogen, which is suitable for a methanation reaction is set by virtue of a corresponding quantity of hydrogen or alternatively carbon dioxide and/or possibly carbon monoxide being supplied, with an auxiliary gas (24), to the exhaust gas (18). Subsequently, a catalytic reaction is performed in which, as starting products, carbon dioxide and/or carbon monoxide and hydrogen are converted into methane and water. The methane is separated off from the product of the catalytic reaction and is subsequently split into carbon and hydrogen, wherein the carbon takes solid form. The split-off carbon is collected and disposed of.