A process is described for separating off a nitrogen-rich fraction from a feed fraction containing essentially nitrogen and hydrocarbons, wherein the feed fraction is separated by rectification into a nitrogen-rich fraction and a methane-rich fraction and wherein the methane-rich fraction for the purpose of cold generation is vaporized and superheated at a pressure as high as possible against the feed fraction which is to be cooled.According to the invention the still liquid or partially vaporized methane-rich fraction (5′) is fed to a circulation vessel (D), only the liquid fraction of the methane-rich fraction (5′) occurring in the circulation vessel (D) is completely vaporized, preferably in natural circulation, and the top product (7) of the circulation vessel (D) is superheated (E1).