In the biological purification of sewage water or drinking water,it is known to purify the water in a filter bed of granular filter medium, wherein the filter medium is transported from the bottom of the bed to its upper side with the aid of air, so as to obtain a continuously working filter. It is suggested in accordance with the invention that the amount of filter medium to be transported is divided into two or more parts which are transported in parallel, so as to prevent the flow conditions in the transport tube having a negative effect on the reactivity of the filter bed by decreasing the bacteria strain.