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An NMR relaxation study of micelles formed in the &(dimethyleicosylammonio)hexanoatt+water system is presented. The zwitterionic surfactant has been specifically labelled with 2H in the position adjacent to the nitrogen on the main hydrocarbon chain, and the 'H NMR relaxation parameters have been determined at nine different magnetic field strengths. In addition,13C relaxation data for the same position in the molecule are presented for three different magnetic field strengths. All the presented NMR relaxation data depend on the magnetic field strength used. The data are analysed with the so-called two-step model, which was originally developed in order to interpret frequency-dependent NMR relaxation data for aggregated surfactant systems. Within the framework of the two-step model two different models for the aggregate motion are discussed, viz. aggregate tumbling and collective fluctuations of the director. Both models are capable of describing the data. In particular, the former model gives a consistent picture with reasonable values of the inherent parameters, provided that the internal motions that the surfactants undergo within the aggregate, have motional components in the nanosecond range. In order to characterize the micelles as regards their size and shape, we also present some small-angle X-ray and fluorescence data for the micelles.