The diffusion process of methane in a silicalite single-crystal membrane has been investigated using the Dual Control Volume-Grand Canonical Molecular Dynamics method. Simulations of full-membrane transport and the three individual contributions that comprise the overall process (entrance to the pores, intra-crystalline diffusion, and exit from the pores) show that the contribution of surface resistance to the overall transport resistance in zeolite membranes is larger and longer range than one might expect. A model is proposed on the basis of the additivity of these contributions. From the individual simulations of exit and entrance zones, it is shown that the adsorption and desorption resistances approach an asymptote with increasing crystal thickness. However, the asymptotic trend has not been observed in full membrane simulations within the thickness limit of this work, possibly because of the coupling between the entrance and exit effects. Since the surface resistance is limited to less than I mum and the single-crystal membrane comprises 100 mum, the surface resistance still represents a relatively small contribution to the overall resistance. Therefore, the diffusion process through the single-crystal membrane is dominated by the internal transport of the sorbate molecules along the principal (z-) axis of the crystal.