Translational diffusion of molecules in one-dimensional channel systems has been measured by quasi-elastic neutron scattering. The scattering function for a single-file diffusion model has been derived in order to differentiate this transport model from normal 1D diffusion. In the AlPO4-5 structure, ordinary 1D diffusion is observed for methane and ethane, whatever the loading, which indicates that the molecules are able to pass each other. The diffusion coefficients for both molecules are on the order of 10(-9) m(2) s(-1). On the other hand, a quite different regime is obtained by varying cyclopropane concentration in the same structure, At low loading, normal 1D diffusion is observed because the molecules can be considered as isolated, but at higher concentration cyclopropane is found to follow single-file diffusion. However, the mobility is too small to be determined. In the less open channel system of ZSM-48, ordinary 1D diffusion is found for small methane concentration, the diffusion coefficient being 2.5 x 10(-9) m(2) s(-1), at 155 K. At medium loading, single-file diffusion is observed with a mobility factor of 2 x 10(-12) m(2) s(-1/2). This is the first rime that this technique has provided experimental evidence of single-file diffusion in zeolites.