Canonical ensemble molecular dynamics simulations of Lennard-Jones methane and ethane are conducted in an atomistic model of AlPO4-5, a molecular sieve with approximately cylindrical channels of diameter 7·3 Å. Methane molecules are able to pass each other in the nanopore and exhibit unidirectional but otherwise ordinary diffusion along the channel axis, with the mean-square displacement directly proportional to time, and a diffusion coefficient calculated at a loading of 0·7 molecules per unit cell at 295 K of 4·70 × 10-4 cm2 s-1. Ethane molecules cannot pass each other easily in the nanopore and for short times exhibit single-file diffusion, i.e., the mean-square displacement is proportional to the square root of the time. After longer times, contributions of ordinary unidirectional diffusion are observed due to the nonzero probability of passing. A slightly larger molecule exhibits pure single-file diffusion. The single-file mobility for the large molecule at 0·7 molecule per unit cell and 295 K is 1·57 × 10-9 cm s-0·5. Effects of fluid density on absorbate mobility are also addressed. The density dependence of the single-file mobility is in agreement with one-dimensional hard rod predictions.