A 6FDA-based, cross-linkable polyimide was characterized in the form of a defect-free asymmetric hollow-fiber membrane. The novel membrane was cross-linked at various temperatures and tested for natural gas purification in the presence of high CO2 partial pressures. The cross-linked membrane material shows high intrinsic separation performance for CO2 and CH4 (selectivity similar to 49, CO2 permeability similar to 161 barrer, with a feed at 65 psia, 35 degrees C, and 10% CO2). Cross-linked asymmetric hollow-fiber membranes made from the material show good resistance to CO2-induced plasticization. Carbon dioxide partial pressures as high as similar to 400 psia were employed, and the membrane was shown to be promisingly stable under these aggressive conditions. The performance of the membrane was also analyzed using the dual-mode sorption/transport model.