Didodecyldimethylammonium bromide (DDAB) in water has been reported to form two coexisting lamellar phases. Here, the phase diagrams of DDAB in H2O and D2O are reinvestigated focusing on the isotopic effect, on the coexistence of two different types of surfactant bilayers at room temperature, and on the structural transition from vesicles to lamellar liquid crystals, observed at low surfactant concentration with increasing temperature. Only at high temperature DDAB forms a monophasic lamellar liquid crystalline structure in the whole range of composition, with critical points located around 84 degrees C in D2O and 74 degrees C in H2O. The higher energy (zero-point stretching) associated with the O-D ... O bond not only increases the transition temperature but also causes the formation of a regular lamellar phase, at room temperature, at a slightly higher surfactant/water molar ratio than in H2O. H-2 NMR data for the DDAB-D2O system evidentiate the temperature dependent structural transition from a L(alpha 1) phase, where lamellar liquid crystals coexist with multilayer vesicles, to a more ordered and apparently homogeneous L(alpha 2) lamellar phase. At 85 degrees C the water molecules, close to the interface, appear to be significantly affected by the surfactant interface, thus displaying a much higher order parameter than at 25 degrees C. The analysis of Br-81 and N-14 NMR data reveals details related to this structural transition which should occur through two main steps. In the range of temperature 30-50 degrees C bromine dissociation plays a crucial role in unsettling the vesicle arrangement whereas in the range 60-85 degrees C the charged bilayers evolve toward a regular lamellar packing. The significant increase of the N-14 quadrupolar splittings with increasing surfactant concentration is interpreted in terms of an increased order of the nitrogen nuclei, which reflects the tendency of the surfactant molecules to assume a more symmetric conformation with respect to the aggregate surface, thus allowing for a higher chain compressibility. The existence of two different stable microstructures, at room temperature, implies that two minima of the self-association energy occur for two different compositions, which, in turn, satisfy two peaking requirements, namely, 0.5 < v.al < 1 (for vesicles) and v/al approximate to 1 (for lamellae).