The Fickian transport diffusivities of binary mixtures of methane and CF4 in the zeolite faujasite were investigated as a function of composition and loading. Using equilibrium molecular dynamics simulations, transport diffusivities of the mixtures were calculated from linear response theory. At low loadings, the diffusive cross terms are an order of magnitude smaller than the diffusive main terms, but at higher loadings they are on the same order of magnitude. The main term diffusivities are weak functions of concentration. The transport diffusivities were fitted as a function of adsorbate concentrations and used in the Fickian flux equations to predict codiffusion, counterdiffusion, and osmotic diffusion through a perfectly crystalline faujasite membrane. The osmotic and counterdiffusion cases show that it is critical to include both the cross term and main term diffusivities to predict the correct behavior. The permeances of methane and CF4 through the faujasite membrane are reported.