NOVELTY - Preparing (M1) crosslinked hollow fiber membrane involves spinning into a monoesterifed fiber a one phase solution comprising a monoesterified polyimide polymer, acetone as volatile solvent, spinning solvent and spinning non-solvent, where the volatile solvent is greater than 25-50 wt.%; and subjecting the monoesterified fiber to one of esterfication and transesterification conditions to prepare a crosslinked hollow fiber membrane.    USE - For preparing crosslinked hollow fiber membrane useful for separating components of gaseous mixture such as methane and carbon dioxide.    ADVANTAGE - The crosslinked hollow fiber membranes have good permeability and selectivity; and good resistance to plasticization. The membranes are durable, resistant to high temperatures, and resistant to exposure to liquids. Subjecting the fibers to transesterification conditions to crosslink the crosslinkable polyimide polymer within the fibers increases both resistance to plasticization and selectivity. The monoesterified hollow fiber formed from monoesterified polyimide polymer having a high average molecular weight, exhibits increased strength and flexibility and can be spun into monoesterified hollow fibers at higher take-up rates. The use of organic solvent such as acetone in relatively high concentrations helps in the formation of relatively thin transition layer between the porous substructure and relatively defect free dense skin of uniform density.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for method (M2) of using a hollow fibers membrane made by method (M1), involving providing feed stream selected from air, mixture of methane and nitrogen, mixture of methane and hydrogen, mixture of methane and hydrogen sulfide, refinery stream, mixture of carbon dioxide and methane, and syngas, the feed stream including gaseous component selected from nitrogen, oxygen, hydrogen, hydrogen sulfide and carbon dioxide; maintaining a pressure differential between an upstream side of the membrane and a downstream side of the membrane; contacting the upstream side of the membrane with the feed stream at 20-4000 psia; isolating a permeate stream on the downstream side of the membrane having a larger mole fraction of the faster permeating component of the feed stream; and isolating a retentate stream having a smaller mole fraction of the faster permeating component of the feed stream.