NOVELTY - Producing methane-rich biogas, comprises: (a) fermenting the biomass in at least one first fermentation vessel (1) during a first fermentation stage to form a raw biogas and a fermentation residue, in which the hydrogenotrophic methanogenic archae-bacteria are present, (b) introducing the raw biogas into a treatment plant and converting the raw biogas into biomethane, by carbon dioxide-containing flue gas which is separated from the raw biogas, and (c) discharging of the fermentation residue from the first fermentation vessel.    USE - The method is useful for producing methane-rich biogas (claimed).    ADVANTAGE - The method: produces product gas with a higher energy content; and provides highest interface for the transfer of the gases in the fermentation medium.    DETAILED DESCRIPTION - Producing methane-rich biogas, comprises: (a) fermenting the biomass in at least one first fermentation vessel (1) during a first fermentation stage to form a raw biogas and a fermentation residue, in which the hydrogenotrophic methanogenic archae-bacteria are present, (b) introducing the raw biogas into a treatment plant and converting the raw biogas into biomethane, by carbon dioxide-containing flue gas which is separated from the raw biogas, and (c) discharging of the fermentation residue from the first fermentation vessel and introducing the fermentation residue into at least one additional fermentation vessel (2) for secondary fermentation of the fermentation residue in a second and/or further proofing step. An INDEPENDENT CLAIM is also included for a plant for producing methane-rich biogas, comprising at least a first fermentation vessel and at least one additional fermentation vessel for secondary fermentation of the fermentation residue in a second and/or further proofing step, a processing plant (5), in which raw biogas is converted into biomethane, by carbon dioxide-containing flue gas, a line which leads from the treatment plant, a hydrogen conduit (9) which is connected to the feed line (8), where the feed line is connected to at least one of the additional fermentation vessel. The carbon dioxide-containing gas from the treatment plant (5) and the hydrogen in the fermentation residue are introduced into the additional fermentation vessel (2), such that the hydrogen is converted to methane by carbon dioxide and hydrogenotrophic methanogenic archae-bacteria present in the fermentation residue during the second and/or additional fermentation stage and a methane-rich product gas is formed.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic representation of a plant for producing biogas.    First fermentation vessel (1)    Additional fermentation vessel (2)    Treatment plant (5)    Feed line (8)    Hydrogen conduit (9)