Abstract: The invention relates to an apparatus for anaerobic purification of waste water, including a reactor space, a supply of influent at the lower side, gas separators and a discharge of gas and a discharge of effluent, respectively, at the upper side of the apparatus. Said apparatus is characterized in that it is in height subdivided into a reactor space, thereabove a sludge-water separator separated from the reactor space and a gas-sludgewater separator above the sludge-water separator separated therefrom, and the apparatus further includes a central tube for recirculating the anaerobic sludgewater material in the reactor space, with the supply for influent at the bottom. Futhermore the present invention also relates to a method for anaerobic purification of waste water with the aid of a suitable anaerobic sludge material, by the use of the apparatus of the invention as mentioned before. Said apparatus and method are particularly suitable for the quick and efficient anaerobic purification of waste water.