The ability of activated carbon to remove mercury and noxious polyorganic matter, especially chlorodibenzo-dioxins and -furans from incinerator flue gases is utilized in an efficient manner by suspending powdery activated carbon in the flue gas in connection with a conventional spray absorption process in which the acidic components of the flue gas are neutralized by means of basic absorbents. The cooling of the flue gases in the spray absorption process provides an efficient adsorption onto the powdery activated carbon and the separation of said powdery activated carbon from the flue gas is substantially facilitated by the presence of the particulate material formed by the spray absorption process. Also an improved removal of nitrogen oxides is obtained.