Process for producing a methane-rich product gas stream at a defined target pressure from a synthesis gas fresh gas stream containing carbon oxides and hydrogen, wherein said process comprises the following process steps: (a) providing a synthesis gas fresh gas stream at an entry pressure, (b) combining the synthesis gas fresh gas stream with a recycle stream to afford a synthesis gas input stream, (c) heating the synthesis gas input stream and supplying to a main reaction zone, (d) reacting the heated synthesis gas input stream to afford a methane-enriched intermediate gas stream in a main reaction zone under methanization conditions, wherein the main reaction zone contains at least one catalyst bed containing methanization catalyst, (e) withdrawing a substream of the methane-rich intermediate gas stream downstream of the main reaction zone as a recycle stream, wherein the recycle stream is recycled upstream of the main reaction zone using a circuit compressor and combined with the synthesis gas fresh gas stream to afford the synthesis gas input stream, (f) supplying the proportion of the methane-rich intermediate gas stream remaining after step (d) to a postreaction zone, (g) converting the intermediate gas stream supplied to the postreaction zone into a methane-rich product gas stream under methanization conditions, wherein the postreaction zone contains at least one catalyst bed containing methanization catalyst, (h) withdrawing the methane-rich product gas stream from the postreaction zone and supplying said stream to a product compressor, characterized in that the main reaction zone and/or the postreaction zone has an auxiliary compressor arranged upstream of it and in that the establishment of the target pressure is effected using the product compressor and the auxiliary compressor. (a) providing a synthesis gas fresh gas stream at an entry pressure, (b) combining the synthesis gas fresh gas stream with a recycle stream to afford a synthesis gas input stream, (c) heating the synthesis gas input stream and supplying to a main reaction zone, (d) reacting the heated synthesis gas input stream to afford a methane-enriched intermediate gas stream in a main reaction zone under methanization conditions, wherein the main reaction zone contains at least one catalyst bed containing methanization catalyst, (e) withdrawing a substream of the methane-rich intermediate gas stream downstream of the main reaction zone as a recycle stream, wherein the recycle stream is recycled upstream of the main reaction zone using a circuit compressor and combined with the synthesis gas fresh gas stream to afford the synthesis gas input stream, (f) supplying the proportion of the methane-rich intermediate gas stream remaining after step (d) to a postreaction zone, (g) converting the intermediate gas stream supplied to the postreaction zone into a methane-rich product gas stream under methanization conditions, wherein the postreaction zone contains at least one catalyst bed containing methanization catalyst, (h) withdrawing the methane-rich product gas stream from the postreaction zone and supplying said stream to a product compressor, characterized in that the main reaction zone and/or the postreaction zone has an auxiliary compressor arranged upstream of it and in that the establishment of the target pressure is effected using the product compressor and the auxiliary compressor.