The invention relates to an apparatus for the conversion into biogas of fermentation stillage arising as a waste product of ethanol production. This apparatus comprises a separation unit for the separation of the fermentation stillage into a thin fraction and a thick fraction, at least one biogas reactor for fermenting the thin fraction and/or the thick fraction, and a storage tank. According to a first aspect of the present invention, two biogas reactors are provided, to separate the thin fraction and the thick fraction independently of one another. According to a second aspect of the present invention, a nitrogen sink is provided downstream of the storage tank to provide, from the reactor effluent, process water with low or no nitrogen content which may then be fed to the reactor and/or the bioethanol plant. According to a third aspect the invention is characterised by a combination of a single-stage separation unit and a heavy-duty biogas reactor with a pore-free flow path.