NOVELTY - Catalytic production of methane-rich gas mixture from sulfur-containing synthesis gas with simultaneous sulfur removal, comprises: producing a synthesis gas mixture; and bringing the synthesis gas mixture into a contact with a methanation catalyst thus continuously deactivating the methanation catalyst by sulfur and/or carbon species comprised in the synthesis gas mixture in one part of the methanation process, while a part of the depleted methanation catalyst is simultaneously regenerated by oxidation in a different part of the process.    USE - The method is useful for catalytic production of methane-rich gas mixture from sulfur-containing synthesis gas.    ADVANTAGE - The method: provides the methane-rich gas mixture, while simultaneously removing sulfur, achieving complete methanation of carbon monoxide and facilitating fast oxidative regeneration of the methanation catalyst and sulfur release; is simple, highly energy efficient requires less unit operations; and utilizes the methanation catalyst that can be used for a long period.    DETAILED DESCRIPTION - Catalytic production of a methane-rich gas mixture from sulfur-containing synthesis gas with simultaneous at least partial sulfur removal, comprises: producing a synthesis gas mixture; and bringing the synthesis gas mixture into a contact with a methanation catalyst thus continuously deactivating the methanation catalyst by sulfur and/or carbon species comprised in the synthesis gas mixture in one part of the methanation process, while a part of the depleted methanation catalyst is simultaneously regenerated by oxidation in a different part of the process. The methanation catalyst is a metal, a metal oxide, a metal sulfide or a mixture of metals, metal oxides or metal sulfide/nitride/phosphide on a support, where the metal or metals are nickel, ruthenium, molybdenum, cobalt, iron, rhodium, palladium, platinum, iridium, osmium, tungsten or vanadium. The support is an oxide comprising alumina, silica, titania, ceria, zirconia, carbides, nitrides and/or phosphides. The metal or metals can be promoted by at least one of the elements comprising potassium, phosphorus, sodium, barium, nickel, ruthenium, rhodium, cobalt, platinum, palladium, iridium, tungsten, osmium, vanadium or manganese.