A model developed for multicomponent gas separation using hollow-fiber contactors permits simulation of cocurrent, countercurrent, and crossflow contacting patterns with permeate purging (or sweep). The numerical approach proposed permits simulation to much higher stage cuts than previously published work and provides rapid and stable solutions for cases with many components, with widely varying permeability coefficients. This new approach also permits the rational and straightforward incorporation of effects such as permeate sweep, pressure-dependent permeability coefficients, and bore side pressure gradients. Simulation results are presented for separation of commercially significant multicomponent gas mixtures using polymer permeation properties similar to those of polysulfone. The effect of permeate purging on separation performance is explored for air separation. The influence of pressure ratio on hydrogen separation performance for a refinery stream is presented. Air is modeled as a four-component mixture of O2, N2, CO2, and H2O and the refinery stream contains five components: H2, CH4, C2H4, C2H6, and C3H8. In air separation, permeate purging with a small fraction of the residue stream provides a very effective method for improving module efficiency for drying but is not efficient for improving nitrogen purity or recovery. In multicomponent mixtures, maxima in the compositions of components of intermediate permeability may be observed as a function of distance along the hollow fiber. This result suggests the use of membrane staging to capture these components at their maximum concentration.