We have investigated how the dynamics of surfactant molecules changes with the vesicle-micelle transition by H-1 NMR relaxation studies on the sodium decyl sulfate (SDeS)-decyltrimethylammonium bromide (DeTAB)-deuterium oxide system. The study has been planned with reference to the phase diagram of the SDeS-DeTAB-water system deduced from thermodynamic analysis of the surface tension data. The spin-lattice relaxation time (T-1) and the spin-spin relaxation time (T-2) are measured at 90 and 400 MHz at various total molalities, m, and compositions, X-2, of the surfactants. The data were analyzed according to the "two-step" model developed by Wennerstrom et al. and molecular dynamics of the surfactant is discussed from the viewpoint of correlation time tau(f) associated with the local fast motion of the surfactant molecule, correlation time tau(s) associated with the slow overall motions of the aggregate and surfactant molecules within it, and local order parameter S. We find tau(s) of vesicles is an order of magnitude larger than that of micelles signifying that the tumbling of vesicle particles and surfactant diffusion over the vesicle are much slower than those for micelle. tau(f) and S for vesicles are also larger than those for micelles. Molecular environments of the surfactant are also discussed from the dependence of the chemical shifts on m at constant X-2 or from that on X-2 at constant m. When the chemical shifts in vesicle and micelle are compared at constant m, the chemical shifts in vesicle are displaced to a lower magnetic field than those in micelle, which implies that the surfactant molecules are arranged more closely to each other in the vesicle than in the micelle.