Abstract: The outgoing gas or waste water is conveyed through a gas-liquid contact apparatus in which biological purification takes place. A bubble plate-type column (2) is used as gas-liquid contact apparatus. The biomass is distributed over the plates (3) in the form of an aqueous suspension with a layer height corresponding to a liquid content per plate greater than 0.07 m.sup.3 /m.sup.2, preferably greater than 0.15 m.sup.3 /m.sup.2 of column cross-section. During the biological purification of gas, the gas to be purified is supplied at the lower end of the bubble plate-type column (2). It then flows through the plates (3) and issues again as purified gas at the top of the plate column (2). When the plate column is used for purifying waste water, the waste water to be purified is conveyed from top to bottom through the plate column (2) and is traversed by air, oxygen or oxygen-containing gas.