Abstract: For the anaerobic fermentation of solid organic waste substances, solid waste is mixed with liquid material, particularly anaerobic slurry, and the temperature of the mixture is brought to a value between 25.degree. and 70.degree. C., preferably between 30.degree. and 40.degree. C. (mesophilic) and between 55.degree. and 65.degree. C. (thermophilic). By means of spontaneous rising of lightweight material and by means of flotation, a layer (10) of solid material floating on a methane-generating zone is formed from said mixture in a reactor. Said floating layer moves from a supply end (7) or a mixing section (2) to a discharge end (14) of the reactor, hydrolysis and acidification of solidorganic material taking place in the floating layer. The fermented floating layer is discharged via the discharge (14) end independent of the residence time of fluid and slurry in the methane-generating zone under the floating layer.