An apparatus for the anaerobic treatment of waste water, including in a same closed enclosure, under a gas pressure, a fermentation zone and a decantation zone, with internal recycling of the slurries from the decantation zone to the fermentation zone, made of at least two attached identical cells in mutual communication. The two cells operate alternately and reciprocally as a fermentation cell and as a decantation cell. Each cell is fitted out, in order to be fed while it operates as a decantation cell, with a gas-lift transfer device with two branches, one of the branches opening into the cell which is attached to that where it is placed.