A process for separating nitrogen from a multicomponent gas mixture containing nitrogen and a hydrocarbon, such as natural gas or associated gas, using gas-separation membranes selective for nitrogen over the hydrocarbon. The membranes use a selective layer made from a polymer having repeating units of a fluorinated polymer, and demonstrate good resistance to plasticization by the organic components in the gas mixture under treatment, and good recovery after exposure to liquid aromatic hydrocarbons.