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The background of and commercial needs leading to the development of practical membrane systems for the separation of industrial gases are presented. The critical issues and fundamental technical limitations that delayed earlier development of such systems and the solutions of some of the major problems in the field are discussed. Particular attention is given to the methods by which high gas fluxes and high selectivities have been achieved in hollow fibers. The performance characteristics of various practical gas separation methods are compared, and the effects of parameters such as pressure and contaminant levels are illustrated with representative examples.