For treating waste gas flows, a regenerative thermal afterburning system is used, comprising at least four regenerators, filled with ceramic heat accumulator bodies, and connected via a common combustion chamber. The waste gas is alternately admitted in cycles to one regenerator, whose heat accumulation bodies have been preheated, and then burned in the combustion chamber to yield clean gas, the said gas being extracted by a further regenerator, with simultaneous heating of the latter's heat accumulator bodies, while a third regenerator is flushed with flush gas. During the cyclical operation of the three regenerators, the remaining fourth regenerator extracts combustion chamber air from the combustion chamber, for the removal of deposits on the heat accumulator bodies in this regenerator by means of pyrolysis. In turn, a fan then feeds this extracted air to the crude gas.