A frequency-dependent 14N and 13C NMR relaxation study of the micellar region formed by a very long zwitterionic surfactant, viz., 6-(dimethyleicosylammonio)hexanoate (C20AH), is presented. As a starting point the binary phase diagram of C20AH/D2O is determined. The phase diagram is similar to those found for shorter chain ionic surfactants with bulky head groups. The NMR relaxation data show a dependence upon the magnetic field strength and are discussed in terms of the two-step model of relaxation. The frequency dependence found at low frequencies in the 14N data is assumed to be caused by the rotational tumbling of the micelle, while it is argued that the frequency dependence found at high frequencies in the 13C relaxation data is caused by a local motion. The analysis of the data yields a radius of the micelle which is slightly shorter than an extended C20 chain, pointing to a situation where the methylene groups in the head-group dipole are embedded in the micelle. Moreover, the local motions in the head-group region are slow as compared to the corresponding motions in single-chain ionic surfactants.