Abstract: A plant for the anaerobic purification of waste and/or process water comprising: i) a reactor tank with at least one feed line for supplying waste and/or process water into tank and with at least one outflow line for draining a mixture of microorganisms, waste and/or process water and gas from the tank, ii) a first separation apparatus outside and downstream of the tank for separating at least a part of the microorganisms from the mixture from the tank, wherein the first separation apparatus comprises at least one separation stage, an inlet line connected with at least one of the outflow line(s), at least one discharge line and at least one outlet line, and iii) a return line for returning the separated sludge separated into the reactor tank, wherein the return line connects with at least one of the at least one outlet line of the first separation apparatus.