Normal and reverse vesicle systems with nonionic surfactants were investigated The solvent selfdiffusion coefficient was measured using the H-1-NMR Fourier transform pulsed gradient spin-echo technique. In the case of normal vesicles, the water solvent is found to exchange rapidly between the inside and outside of the vesicles on the experimental time scale (approximate to 0.1 s). Here, only an average self-diffusion coefficient can be measured from which the fraction of entrapped water can be determined. In the reverse vesicle case, we observe either a fast or a slow exchange, depending on the oil and the bilayer composition. In particular we have investigated a semipermeable membrane system, where with a solvent mixture, one of the two types of solvent molecules exchanges fast while the other exchanges slowly on the experimental time scale. Here, the lifetime of a solvent molecule inside the reverse vesicles was found to depend on the composition of the mixed reverse bilayers, leading to an observed transition from fast to slow exchange conditions when varying the bilayer composition. In the slow exchange case, the self-diffusion coefficients of solvent molecules on the outside and inside of the vesicles, where the latter reports on the vesicle self-diffusion coefficient, are in principal resolved. From the bimodal type of decay of the spin-echo amplitude, it is also possible to determine directly the fraction of solvent molecules entrapped inside the vesicles.