Abstract: A reactor for catalytically converting gases containing carbon oxides, hydrogen and water vapor into methane under elevated temperatures and pressures. The reactor includes a substantially cylindrical outer shell which is provided at opposite end faces with a gas inlet and a gas outlet. An inner vessel contains part of the catalyst volume for the reactor which is impermeable to gas adjacent to the gas inlet. The inner vessel has a substantially cylindrical shell which defines a flow passage with the inner surface of the outer shell of the reactor and has openings for the radially inward passage of the gas mixture to be reacted. A perforated central gas-collecting tube containing no catalyst is positioned in the inner vessel and one or preferably two additional catalyst beds are positioned between the inner vessel and the gas outlet.