The motion of molecules captured inside the rods of hexagonal phases of several water-in-oil (w/o) and oil-in-water (o/w) didodecyldimethylammonium sulfate/bromide-hydrocarbon-water systems has been measured by using the pulsed field gradient (PFG) NMR technique. The self-diffusion of hexadecane and dodecane in the case of o/w aggregates, as well as water in the case of w/o aggregates, has been investigated at different diffusion times. It was found that only for the oil-in-water aggregates could the true self-diffusion coefficients for translational motion along the cylinder axis be obtained, on account of the rms displacement during the NMR time scale of the oil molecules being smaller than the surfactant aggregate microdomains. The results show that the self-diffusion coefficient for hexadecane is reduced by a factor of roughly 10, while for dodecane only by a factor of roughly 5, as compared to the respective bulk self-diffusion coefficient. Possible reasons for the reductions are discussed.