Aqueous binary systems of potassium oleate and sodium dodecyl sulphate exhibit an hexagonal phase at low surfactant concentrations and appropriate temperatures. However, in the former system the phase is succeeded at higher surfactant concentrations by the so-called rectangular phase, while in the latter system a distorted hexagonal phase follows. X-ray diffraction results for these systems indicate that the rectangular phase is a consequence of axial growth of the hexagonal-phase surfactant cylinders with surfactant content at substantially constant radius. Water in the hexagonal phase occupies positions other than along and between cylinder lengths. Radial growth of cylinders leads to the distorted hexagonal structure. The cylinder growth and transformation behaviours are associated with characteristics of the respective molecular structures.