NOVELTY - The method of producing methane-rich gas from a synthesis gas (4), comprises mixing a carbon monoxide (CO) and hydrogen (H2)-c ontaining synthesis gas with a gas stream (8) branched off and reduced to the methane-rich product gas and then guiding through a catalyst bed (1) from a methanation catalyst. The methanation is carried out in the catalyst bed, and a heat of reaction heats the gas stream. The catalyst bed is successively divided to flow through a methanation step (2.1), and the synthesis gas is divided corresponding to partial flows.    USE - The method is useful for producing methane-rich gas from synthesis gas.    ADVANTAGE - The method is capable of effectively and economically producing the methane-rich gas from the synthesis gas with less effort.    DETAILED DESCRIPTION - The method of producing methane-rich gas from a synthesis gas (4), comprises mixing a carbon monoxide (CO) and hydrogen (H2)-containing synthesis gas with a gas stream (8) branched off and reduced to the methane-rich product gas and then guiding through a catalyst bed (1) from a methanation catalyst. The methanation is carried out in the catalyst bed, and a heat of reaction heats the gas stream. The catalyst bed is successively divided to flow through a methanation step (2.1), and the synthesis gas is divided corresponding to partial flows, which are fed to the catalyst bed of an associated methanation step. After the completion of the methanation step, heated gas is mixed with partial flow of the synthesis gas in the methanation reaction followed by cooling for subsequent methanation. The resulting mixed gas flow to the catalyst bed of the subsequent methanation step is fed as feed gas. The gas stream branched off and reduced from the methane-rich product gas: is fed to the catalyst bed of the first methanation step; and is divided into partial flows, which are fed to the methanation step. A mixing gas temperature is adjusted by 300 degrees C in the feed gas fed to the methanation step. An amount of the gas stream fed to the first methanation step corresponds to 2-4 times of the amount at the synthesis gas, which is fed as the partial flows of the total flow at the synthesis gas of the first methanation step. In the first methanation step and the conversion step, 2-5% of the synthesis gas is fed as feed gas. The temperature and flow rates of the gas stream brought together before the methanation step under consideration of the resulting methanation reaction are coordinated such that the methane-rich gas emerging from the methanation step exhibits an outlet temperature of less than 800?C. The first methanation step of a CO-conversion step (3) is upstream to a CO-conversion catalyst and is branched off from the synthesis gas of the synthesis gas partial flow, which is fed to the CO-conversion step, which is fed to a steam and to the partial flow of the reduced gas stream. The total amount of the gas stream reduced to the CO-conversion step and the first methanation step corresponds to 2-4 times of the amount at the synthesis gas, which is fed as the partial flow of the total flow at the synthesis gas of the CO-conversion step and/or the first methanation step. The synthesis gas partial flow is fed with a temperature of 200-250 degrees C of the CO-conversion step. After the completion of the CO-conversion step, the gas stream is mixed before entry into the subsequent methanation step of the synthesis gas partial flow and a portion of the reduced gas stream so that it gives a mixing temperature, which is greater than or equal to a light-off temperature for the methanation in subsequent methanation step, where the resulting mixed gas temperature is greater than 300 degrees C. The synthesis gas partial flow is fed for cooling the methane-rich gas with the temperature of less than 250 degrees C emerging from the methanation step. An INDEPENDENT CLAIM is included for a methanation reactor for producing methane-rich gas from synthesis gas.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a methanation reactor for producing methane-rich gas from synthesis gas.    Catalyst bed (1)    Methanation step (2.1)    CO-conversion step (3)    Synthesis gas (4)    Methane-rich product gas (7)    Gas stream. (8)