Aqueous solutions of the nonionic surfactant, n-dodecylhexaoxyethylene glycol [C12H25(OCH2CH2)(6)OH], termed C12E6, form various phases at room temperature: there is a micellar phase at high water content, hexagonal, cubic, and lamellar mesophases at intermediate water contents, and an isotropic phase at very low water content. Proton nuclear magnetic resonance (NMR) T-1(-1) relaxation rates have been measured for the C12E6/D2O system as a function of composition, spectral frequency, and temperature. The results are interpreted in terms of the possible molecular motions for the C12E6 molecule in the different phases. A review of relaxation theory is presented with special attention to molecular exchange between sites that are associated with different relaxation rates.