In a process for the conversion of a synthesis gas mixture containing hydrogen, carbon oxides and at least one other gas to a methane-containing gas mixture by catalytic conversion, the improvement wherein said synthesis gas mixture contains at least one gaseous sulfur compound in an amount of at least 10 ppm, calculated as H.sub.2 S, and said conversion is conducted at a temperature of 250.degree.-850.degree. C. and a pressure of 1-150 bar in the presence of a catalyst consisting of at least one component selected from the group consisting of vanadium and molybdenum, salts, oxides and sulfides thereof, said catalyst being deposited on a support consisting of porous titanium dioxide, whereby the product gas mixture contains at least 50%, by weight, of methane based on the amount of carbon in said synthesis gas mixture converted to hydrocarbons.