NOVELTY - A raw material is separated into gaseous and liquid components. The gaseous component is separated into hydrogen and low-pressure methane fractions, and liquid component is separated as hydrocarbon fraction. While separating gaseous component as high-pressure methane fraction, liquid component is further separated as medium-pressure methane fraction. By supplying nitrogen-oxide-containing light gas to de-methanizer (61) in cooling system (1) with heat exchanger (41), hydrocarbon fraction is separated by exchanging heat with hydrogen and methane fractions.    USE - For separating 2C or more hydrocarbon fraction containing useful olefin fractions, such as ethylene and propylene, from nitrogen-oxide-containing light gas, such as fluid catalytic cracking off gas by-produced in petroleum-refining processes.    ADVANTAGE - The method enables efficient separation of 2C or more hydrocarbon from light gas, suppressing generation and deposition of nitrogen-oxide rubber. Since the supply of liquid-phase component is continued by the nitrogen-oxide-containing light gas stripper even when the supply of fluid catalytic cracking off gas is stopped, the operation of the stripper is continuable and the influence of the fluctuation of petroleum-refining plant-operation conditions is decreased.    DETAILED DESCRIPTION - A raw material containing hydrogen, methane, and 2C or more hydrocarbon is supplied to a vapor-liquid separation tank (31-34) which separates the raw material into a gaseous-phase component and a liquid-phase component. The gaseous-phase component is separated into a hydrogen fraction and a low-pressure methane fraction in a hydrogen-low pressure methane separation tank (51), and the liquid-phase component is distilled and separated as a 2C or more hydrocarbon fraction in a de-methanizer (61). The component from the top of the de-methanizer is cooled. While separating the gaseous-phase component as high-pressure methane fraction, the partial liquid-phase component is further separated as a medium-pressure methane fraction. The remaining gaseous-phase component is then re-circulated to the de-methanizer by a reflux tank (71). By supplying the nitrogen-oxide-containing light gas to the de-methanizer in a cryogenically-cooling system (1) equipped with cryogenically-cooling heat exchanger (41), the 2C or more hydrocarbon fraction in the light gas is separated by exchanging heat with hydrogen fraction and low-pressure-medium-pressure-high-pressure methane fraction.    DESCRIPTION OF DRAWING(S) - The figure shows the structure of the cryogenically-cooling system.    Cryogenically-cooling system (1)    Vapor-liquid separation tank (31-34)    Cryogenically-cooling heat exchanger (41)    Hydrogen-low pressure methane separation tank (51)    De-methanizer (61)    Reflux tank (71)