The aim of the present invention is to keep the solid content of the washing mixture generally constant, notwithstanding variations in the SO2 concentration, in a known process with prewash stage for separating HF, HCl and a subsequent, in the direction of the gases, main-wash stage for separating SO2, whereby in both these stages a washing solution is fed into the circuit and in the main-wash stage, after washing, droplets are separated from the waste gas by means of a mist collector and in case of a fault, the washing solution is evacuated from the washing basin of the main-wash stage through an overflow and washing solution from the main-wash stage containing solids is extracted and the water removed. The additional water (22) required for operating the mist collector nozzles (14) is provided in a quantity depending on the volume of waste-gas (7) to be purified, washing solution is extracted from the washing basin subject to the quantity of SO2 separated, part of the washing solution (30) is taken from the main-wash stage (8) circuit (9) and at least partially clarified; finally, the part with the greater solid content (23) is fed back into the main-wash stage (8) and the part with the smallest solid content (31) is evacuated.