The flue gas scrubbing system comprises multiple stages in which gaseous pollutants and heavy metals are removed from the flue gas. The wet scrubber cleans up the flue gases reliably and with minimal doses of consumables even when the pollutant burden is high. Residues are extremely small in quantity. The pollutant-laden water is neutralized and either purified or concentrated by evaporation. The result is emission values just a fraction as high as the most stringent limits.