Molecular transport in nanoconfined spaces plays a key role in many emerging technologies for gas separation and storage, as well as in nanofluidics. The infiltration of fluid mixtures into the voids of porous frameworks having complex topologies is common place to these technologies, and optimizing their performance entails developing a deeper understanding of how the flow of these mixtures is affected by the morphology of the pore space, particularly its pore size distribution and pore connectivity. Although several techniques have been developed for the estimation of the effective diffusivity characterizing the transport of single fluids through porous materials, this is not the case for fluid mixtures, where the only alternatives rely on a time-consuming solution of the pore network equations or adaptations of the single fluid theories which are useful for a limited type of systems. In this paper, a hybrid multicomponent effective medium-correlated random walk theory for the calculation of the effective transport coefficients matrix of fluid mixtures diffusing through porous materials is developed. The theory is suitable for those systems in which component fluxes at the single pore level can be related to the potential gradients of the different species through linear flux laws and corresponds to a generalization of the classical single fluid effective medium theory for the analysis of random resistor networks. Comparison with simulation of the diffusion of binary CO(2)/H(2)S and ternary CO(2)/H(2)S/C(3)H(8) gas mixtures in membranes modeled as large networks of randomly oriented pores with both continuous and discrete pore size distributions demonstrates the power of the theory, which was tested using the well-known generalized Maxwell-Stefan model for surface diffusion at the single pore level.