Abstract: In a two-stage process for the biological degradation of complex, non-readily degradable wastewater constituents, acidification takes place in the first stage and anaerobic degradation in the presence of methanogenic organisms in the second stage. In the first stage, the wastewater is treated both with the acidogenic organisms and with dehalogenating and/or desulfonating and/or deaminating strains. In addition, highly sub-stoichiometric quantities of oxygen, based on the organic carbon load, are introduced in the first stage either directly or indirectly by addition of oxygen-yielding compounds. Both stages are advantageously operated as fluidized-bed processes using supports to immobilize the biomass.