The microemulsion phase in the didodecyldimethylammonium sulfate/hydrocarbon/water system was investigated with NMR self-diffusion, 2H NMR relaxation, and the time-resolved fluorescence quenching technique. From the NMR self-diffusion experiments, it was found that the diffusion of the surfactant and the hydrocarbon are equal for a certain range of surfactant to oil concentration ratios, indicating that in this range of composition the structure is one of discrete aggregates. Upon an increase of the surfactant to oil volume ratio, there is an onset of a network formation, as indicated by the fact that the surfactant self-diffusion is smaller than that of the hydrocarbon. Close to the lower values of the oil to surfactant concentration ratio for which the microemulsion exists, a bicontinuous micellar network is formed. Phase studies and self-diffusion experiments in mixtures of a microemulsion with normal curvature, that is, with sulfate as counterion, with a microemulsion with reversed curvature, that is, with bromide as counterion, showed that the ratio of the two counterions can be used to tune the curvature of the surfactant film. Reasons for this behavior are discussed. Finally, based on NMR relaxation and NMR diffusion experiments, a value for the lateral diffusion of surfactant along the surfactant film is derived.