A double- tail amine oxide surfactant, di- n- decylmethylamine oxide ( 2C10MAO), was prepared, and the effects of protonation on aggregate structure were examined by small- angle neutron scattering ( SANS), cryotransmission electron microscopy ( cryo- TEM), turbidity, electric conductivity, and solubilization of an oil-soluble dye at various degrees of neutralization, X, defined as the mole ratio of HCl/ 2C10MAO. The surfactant makes an L-2 phase in the nonprotonated state ( X = 0) in water. The L-2 phase is in equilibrium with an aqueous L-1 phase. On protonation, unilamellar vesicles ( ULVs) are formed over a wide range of compositions ( 0.05 < X< 0.4- 0.5 at C = 10 mM) as observed by cryo- TEM. At X = 0.2, the ULV is stable over a wide concentration range ( 3 mM <= C < 0.1 M), but an L-alpha phase replaces the vesicle phase at C > 0.1 M. SANS results show that the mean radius of the ULV is about 25 nm and the bilayer thickness is about 2 nm, consistent with the extended configuration of the alkyl chains of the surfactant. An important contribution to the enhanced stability of the bilayer structures over the L-2 phase is suggested to be the translational entropy of the counterions. The enhanced stability of the bilayers diminishes as the counterion concentration increases either by an increase of X or by the addition of a salt. When the counterion concentration exceeds a critical value, the ULV solutions transform into the L-2 phase ( or L-2/ L-1 two- phase system at low surfactant concentrations). The critical composition X* is about 0.4- 0.5 in water, but it is below 0.4 in D2O. The critical NaCl concentration is below 5 mM at X = 0.2. The stability of ULVs against multilamellar vesicles is ascribed partly to undulation forces and partly to the adjustable nature of the spontaneous curvature of amine oxide monolayers. The characteristics of the ULV of the surfactant remain the same within a temperature range 25 - 50 degrees C at X = 0.2. An iridescent lamellar phase and possibly an L-3 phase were observed in a very narrow X range ( 0 < X < 0.02) prior to the vesicle phase.