NMR spectroscopy is employed to study the aggregation of a cationic surfactant, 4-aza-1-cetyl-1-azoniabicyclo[2.2.2]octane bromide, in aqueous solutions. Self-diffusion coefficients are determined for micelles and monomers and the hydrodynamic radius and aggregation number are calculated for micelles. Polarization microscopy data demonstrate that the examined compound is an amphotropic substance. It is found that the lyotropic liquid-crystalline system is characterized by a wider temperature range of mesophase existence as compared to the thermotropic system.