The phase behavior of a very dilute aqueous solution of a sodium decyl sulfate (SDeS)-decyltrimethylammonium bromide (DeTAB) mixture was investigated by the surface tension measurement and partly by the density measurement. The surface tension gamma and density rho were measured as functions of total molality of surfactants (m) over cap and composition of DeTAB (X) over cap(2). Break points were observed on the curves and identified as the critical vesicle concentration and the concentrations of the initial and final points of the vesicle-micelle coexisting region, respectively. These break points were plotted against (X) over cap(2), analyzed thermodynamically, and then compared with the ones in the diagrams predicted from a simple model. The composition of DeTAB in the vesicles at the critical vesicle concentration (cvc) was obtained from the eve versus (X) over cap(2) curve, and it was found out to be 0.5 at almost all (X) over cap(2) values. From the other break point versus (X) over cap(2) plots, the composition region of the vesicle-micelle coexistence in the phase diagram was suggested to be from 0.62 to 0.65. Furthermore, vesicle formation was clearly indicated to take place even at (X) over cap(2) = 0.9999, and therefore, the vesicle-micelle transition on the critical aggregation concentration (C) over cap versus (X) over cap(2) curve was expected to sit between (X) over cap(2) = 0.9999 and 1.