Abstract: A method for biological purification of water such as wastewater using a carrier material is disclosed, wherein the water is treated in a reactor containing carriers for biofilm growth. These carriers are kept in movement in the water and are designed so that they have well-defined passages or compartments providing a surface for biofilm growth, which is protected against collision with the surfaces of other carriers. The carriers have a width or diameter greater than 20 mm, the protected area is larger than 1000 m2/m3 carrier element volume, the length of the passages or the depth of the compartments in the carrier elements as a mean value is smaller than 6 mm or smaller than 3 mm, respectively, and the ratio between the passage lengths or compartment depths and the longest dimension of the inlet openings to the passages or compartments, respectively, is smaller than 3.