SO.sub.2 and/or NO.sub.x are removed from gaseous CO.sub.2 at elevated pressure(s) in the presence of molecular oxygen and water and, when SO.sub.2 is to be removed, NO.sub.x, to convert SO.sub.2 to sulfuric acid and/or NO.sub.x to nitric acid. The sulfuric acid and/or nitric acid is/are then removed from the gaseous carbon dioxide to produce SO.sub.2-free, NO.sub.x-lean carbon dioxide gas. The invention has particular application in the removal of SO.sub.2 and/or NO.sub.x from carbon dioxide flue gas produced in an oxyfuel combustion process, for example, in a pulverized coal fired power station.