Process for producing synthetic natural gas (SNG) which is provided in an energy-efficient way at the inlet pressure into a downstream pipeline system. For this purpose, a synthesis gas containing carbon oxides and hydrogen is converted into a product gas rich in methane by multi-stage catalytic methanation in a main reaction zone and a post-reaction zone, wherein the adjustment of the target pressure is effected by compression before the main reaction zone and/or before or in the post-reaction zone.