Abstract: In the introduction of a finely dispersed gas containing at least about 20 to 45% of oxygen by volume with intensive mixing into a vessel having a gas space and effluent containing biochemically oxidizable constituents, in the presence of activated sludge, the improvement which comprisesA. introducing oxygen into the gas space of said vessel in such amount that the oxygen content is within 10% of a predetermined value;B. a component volume of the gases in the gas space being ejected as a fine dispersion into the effluent, andC. directly introducing oxygen into the component volume being ejected into the effluent in such amount that the oxygen content in the effluent is within 60% of a predetermined value, whereby there is obtained an improved utilization of oxygen even in the event of fluctuations in load of the effluent. Advantageously the effluent from the first vessel cascades into a second vessel which is similarly treated.