NOVELTY - Catalytic methanisation of a gas mixture comprising hydrogen and carbon dioxide, comprises: (a) introducing the gas mixture into a first reactor stage (9); (b) carrying out catalytic methanisation of the gas mixture; (c) partially removing the water emerging from the gas mixture contained in the first reactor stage by cooling to 80-160 degrees C and removing the condensed water from the reactor system during the cooling with a condensate discharge (17); (d) introducing the gas mixture into the second reactor stage; and (e) carrying out post-methanisation of the gas mixture.    USE - The methane rich gas mixture is useful as a fuel for power vehicles or as a feed into the German natural gas network.    ADVANTAGE - The method: shows high efficiency catalytic synthesis of methane from gas mixture comprising carbon dioxide and hydrogen at low pressure, thus it provides long lifetime to the catalyst; comprises partial removal of water from the gas mixture, thus it extends the lifetime of the catalyst; leaves some quantity of water in the gas mixture, which increases the methane yield even at moderate pressures; exhibits continuous increase in temperature from input to output of the reactor stage and favors the exothermic hydrogenation of carbon dioxide, which shifts the equilibrium to the product side, thus it exhibits improved efficiency of the methanation; and utilizes the gas mixture with a carbon monoxide content of less than 0.1% and thus it reduces the carbon deposits on the catalyst surface.    DETAILED DESCRIPTION - Catalytic methanisation of a gas mixture comprising hydrogen and carbon dioxide, which has a carbon monoxide content of less than 0.1%, in a reactor system (1) from at least two sequentially arranged reactor stages comprising a catalyst respectively, comprises: (a) introducing the gas mixture into a first reactor stage (9) of the two sequentially arranged reactor stages; (b) carrying out catalytic methanisation of the gas mixture at 300-600 degrees C in the first reactor stage; (c) partially removing the water emerging from the gas mixture contained in the first reactor stage by cooling to a temperature of 80-160 degrees C below the dew point and removing the condensed water from the reactor system during the cooling with a steam trap (17) arranged between the first and the second stage reactor (10); (d) introducing the gas mixture from which the water obtained in the step (c) is partially removed in the second reactor stage; and (e) carrying out post-methanisation of the gas mixture at 250-300 degrees C in the second stage reactor. An INDEPENDENT CLAIM is also included for the methane-rich gas mixture obtained by the above mentioned method.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic flow diagram of the reactor system for carrying out the method.    Reactor system (I)    Synthesis unit (3)    First reactor stage (9)    Second reactor stage (10)    Steam trap (17)