A process is described for removing a nitrogen-rich fraction from a feed fraction containing essentially nitrogen and hydrocarbons, wherein the feed fraction is partially condensed and fractionated by rectification into a nitrogen-rich fraction and a methane-rich fraction.According to the invention during an interruption in the supply of the feed fraction, the separation column(s) (T1/T2) used for the fractionation by rectification and also the heat exchangers used for the partial condensation (E1) of the feed fraction and the cooling and warming of process streams occurring in the fractionation by rectification (E2) are kept by means of one or more differing cooling media (6-11) at temperature levels which correspond essentially to the temperature levels during standard operation of the separation column(s) (T1/T2) and the heat exchangers (E1, E2).