Abstract: A method of purifying flue gas from the firing equipment of a combustion unit, especially fuel gas from fitting equipment to which low-ash flue is supplied, or from a grating firing having a high degree of ash removal, with the flue gas containing noxious compounds. A finely divided or pulverous basic additive is used on which the noxious compounds produced during firing are adsorbed. Flue dust, especially flue dust/additive mixture, that is carried along in the flue gas is separated from the latter, with at least a portion of the separated-off flue dust being hydrated and sifted, whereby subsequently at least a portion of the dry, hydrated flue dust is returned to the flue gas purification process. Non-pulverized flue dust is homogenously mixed with finely sprayed water to effect the hydration. The return of flue dust to the flue gas purification process is undertaken by returning at least a portion of dry, thus-hydrated flue dust to the firing equipment of the combustion unit.