Several different samples of sodium dodecyl sulfate (SDS, anionic surfactant) and dodecyltrimethylammonium bromide (DTAB, cationic surfactant) in D2O at 40 degrees C in the absence of added salt have been studied using small-angle neutron scattering (SANS). The surfactant molar ratios of SDS and DTAB ranges between 15:85 and 40:60 and between 60:40 and 85:15, and the total amount of surfactant ranges between 0.125 and 5 wt %. The scattering data were fitted by various models for geometrically differently shaped particles using conventional least-squares methods. Small unilamellar vesicles (350 Angstrom < [R-v] < 650 Angstrom) were found in the very dilute samples of compositions 15:85-25:75 and 75:25-85:15 whereas larger oligolamellar vesicles predominate in the dilute samples nearer equimolar surfactant composition. When the overall surfactant concentration is increased above 0.25-1.0 wt %, depending on composition, we observe evident transitions either from small unilamellar vesicles to micellar aggregates or from larger oligolamellar vesicles to lamellar sheets. In connection with this, the transition from rod-shaped micelles, via disk-shaped micelles, to large lamellar sheets is observed as the surfactant composition approaches equimolarity from compositions of both 15:85 and 85:15, at a fixed overall surfactant concentration above the limit where no vesicles form. The experimental results are discussed and rationalized from the viewpoint of a simple thermodynamical model. In particular, the theory predicts an abrupt transition from small disk-shaped micelles to almost infinitely large lamellar sheets, as the surfactant composition is slightly changed toward equimolarity at a certain overall surfactant concentration, in agreement with the experimental observations.