The effects of nanoparticles on the rates of gas diffusion through glassy polymers were studied by a combination of molecular dynamics and kinetic Monte Carlo techniques designed to overcome the computational limitations in obtaining long-time trajectories in the diffusive regime of gas molecules in glassy polymer systems. Using such a methodology, we studied the effect of fullerene nanoparticles upon the diffusivities of N(2) and CO(2) in a polystyrene matrix. The addition of nanoparticles was found to cause a lowering of the diffusion coefficients of both N(2) and CO(2). However, the magnitudes of this lowering and their volume fraction dependencies are seen to depend explicitly on the nature of the penetrant and temperature. We discuss the possible physical mechanisms underlying such behavior.