We have used nonequilibrium molecular dynamics (NEMD) simulations to evaluate diffusivities for binary mixtures of methane/CF4, propane/CF4, n-butane/CF4, and n-butane/ethane in zeolite faujasite at 300 K. A formula to estimate the error bars in the transport coefficients from NEMD is also presented. NEMD simulations can give cross coefficients of the Onsager matrix with considerably smaller error bars than those obtained from equilibrium MD (EMD). We evaluated diffusion coefficients that could not be evaluated previously using EMD. An estimation scheme based on the Maxwell-Stefan formulation was tested for predicting multicomponent diffusivities based on single component diffusion data. This estimation scheme works very well for the systems tested.