A plug-flow operated, horizontal fermenter for anaerobic fermentation of biogenic waste includes a fermenter tank having an inlet and an outlet that is configured to be filled with a biomass material. The fermenter also includes an agitator having a shaft passing through the fermenter tank in its longitudinal direction, wherein the shaft is mounted in end regions of the fermenter tank and is designed as a closed, hollow shaft having an inner space filled with gas or air. A plurality of agitator arms are arranged on the shaft. The inner space of the shaft is monitored with respect to a gas or air pressure to ensure that a buoyancy of the shaft in the filled fermenter tank at least approximately compensates for a sagging of the shaft.