A process for the co-production of superheated steam and methane includes reacting a gas containing carbon monoxide and hydrogen in a series of methanation regions to produce a product gas containing methane The gas containing carbon monoxide and hydrogen flows, in passing through the series of methanation regions, successively through at least a first internally cooled methanation region and a second internally cooled methanation region, cooling the first and second internally cooled methanation region with water, which water is vaporized in the first internally cooled methanation region to produce steam and which steam is subsequently superheated in the second internally cooled methanation region to produce superheated steam The internally cooled methanation regions include tubes filled with a methanation catalyst and a space surrounding the tubes The gas containing carbon monoxide and hydrogen and/or product gas flows through the tubes and the water flows through the space surrounding the tubes.