Results for the permeation of binary mixtures through a silicalite-1 membrane are presented. The binary separation factor for mixtures of CH4–N2, CO2–N2, and CO2–CH4 is studied as a function of the feed composition and as a function of the feed pressure. A comparison is made between the separation factor calculated from the binary fluxes and the so-called ideal separation factor, which is given by the ratio of the one-component flux. In general, the binary separation cannot be predicted from the one-component data alone. At ambient temperature the separation obtained with the silicalite-1 membrane is based on a difference in equilibrium adsorption. It is found that the separation factor is a function of both the composition and the pressure. The fact that the separation factor varies with the feed composition and the feed pressure cannot be explained with the extended Langmuir model used to describe the binary equilibrium adsorption. A reasonable description of the separation factor as a function of the pressure and composition is possible with the ideal adsorbed solution theory. Using the permeation and separation properties for the CO2/N2/silicalite-1 system a membrane cascade is designed. The surface area of the membrane cascade has been calculated with both the binary and the ideal separation factor.