Abstract: A method and an apparatus for the purification of waste air containing biologically decomposing impurities. The waste water is conducted through an absorption tower in which the impurities are absorbed by washing liquid containing an activated sludge. Subsequently, the impurities are biologically decomposed in an activated sludge basin by the microorganisms of the activated sludge. To ensure that the residual amount of washing liquid to be removed is small and only a small amount of biological excess sludge is produced even if large amounts of impurities must be decomposed, while the activated sludge basin remains relatively small, the waste air is subjected to a preliminary purification in at least two successive stages by means of a highly polluted washing liquid. Subsequently, the waste air is subjected to an after purification by means of an only lightly polluted washing liquid. The two different washing liquids are then conducted in a cascade-like manner through separate activated sludge basins.