Pulsed field gradient spin-echo (PGSE) FT-NMR experiments have been performed in order to characterize the structure of a reverse hexagonal lyomesophase of a nonionic surfactant-water-oil system, weakly charged. The nonionic surfactant system contains pentaethylene glycol dodecyl ether (C12E5), water, decane, and small amounts of an ionic surfactant, sodium dodecyl sulfate (SDS). The observed spin-echo attenuation due to water self-diffusion at different temperatures and compositions has been interpreted with a one-dimensional diffusion model, i.e., a self-diffusion in randomly oriented array of capillaries with both transverse dimensions <100 nn. By combining self-diffusion and apparent self-diffusion coefficients, we calculated diffusional "obstruction factors" of about 1/3 and confirmed the presence of a reverse hexagonal microstructure. Unrestricted diffusion behavior has been observed performing PGSE experiments as function of diffusion times. As a consequence, a reverse hexagonal phase with aggregates consisting of essentially infinite cylinders has been hypothesized.