Gump et al. (Ind. Eng. Chem. Res. 1999, 38, 2775) recently showed that extremely high selectivities are realized for the separation of normal hexane (n-C-6) from 2,2-dimethylbutane (22DMB) when these components are allowed to diffuse across a ZSM-5 zeolite membrane. Their reported selectivities for a 50-50 feed mixture was found to be about 2 orders of magnitude higher than that for the single components. Furthermore, at a temperature of 398 K, the flux of 22DMB exhibits a curious maximum with increasing partial pressure. The objective of this communication is to provide a theoretical background to their experimental observations. Configurational bias Monte Carlo (CBMC) simulations are used to calculate the pure component and mixture isotherms at various temperatures. The Maxwell-Stefan (MS) theory for zeolite diffusion is then used to calculate the fluxes for single-component and binary-mixture permeation. The combined CBMC-MS model provides a nearly quantitative explanation of the experimental data of Gump et al.