Diffusivities of methane, ethane, propane and n-butane for silicalite-1 membranes, consisting of intergrown crystals, were determined from permeation measurements. Experiments were conducted according to a batch method and the Wicke–Kallenbach method. The temperature of the experiments was varied between 273 and 673 K, and (partial) pressures from 10 to 425 kPa were applied. The model used was based on two contributions to transport through the membrane, viz., intracrystalline diffusion and activated gaseous diffusion. The Darken thermodynamic correction factor was applied to obtain the corrected transport diffusivity for intracrystalline diffusion. The single-component fluxes through the membrane could adequately be described using this two-contribution model. Diffusivities obtained from the Wicke–Kallenbach method at lower loadings were lower than those obtained from the batch method, owing to the back-permeation of the sweep gas in the Wicke–Kallenbach method. A slight occupancy dependence is observed for the intracrystalline diffusivities below 0.9. Above an occupancy of 0.9 these values decrease. For methane and ethane the temperature dependence of the intracrystalline diffusivity was in agreement with literature data for self-diffusion. For propane and n-butane up to 100 times lower values for the diffusivity were found, and for these molecules a higher activation energy was observed than that for the self-diffusivity. These lower values and higher activation energy of the membrane diffusivities are attributed to additional energy barriers in the membrane. Diffusion through a layer of intergrown zeolite crystals is not identical to diffusion in single zeolite crystals and must be determined individually. There is considerable room for improvement of the membrane, both by optimizing the zeolite layer and the mesoscopic structure of the support.