The properties of L(2) phase and cubic phase in the ternary system AOT/1-octanol/water have been studied by means of electrical conductivity, NMR self-diffusion experiments, theology, static and dynamic light scattering, SANS, and DSC. L(2) phase and cubic phase are neighboring phases that are both isotropic but vary largely with respect to their macroscopic appearance; i.e., the L(2) phase is of low viscosity, whereas the cubic phase is gel-like. At the phase transition, L(2) phase --> cubic phase, no discontinuities were observed for the electrical conductivity and the self-diffusion coefficient of water; i.e., both phases should structurally be closely related and both are bicontinuous. SANS showed that in the cubic phase the size of the structural units decreases with increasing AOT concentration. The self-diffusion coefficients of both water and octanol/amphiphile are decreasing in parallel with the size of the structural units. At the same time the shear modulus rises with increasing surfactant concentration, which can be explained in terms of a simple network theory, where each structural unit acts as a network point. At high temperatures the cubic phase melts to form the L(2) phase with transition enthalpies of typically 5-250 mJ/g. Finally, it was observed that for not too high AOT content such a phase transition occurs also upon lowering the temperatures; i.e., a reverse melting transition takes place.