Fluorescence depolarization techniques are used to determine the molecular order and reorientational dynamics of the probe molecule TMA-DPH embedded in the lamellar L alpha and the hexagonal HII phases of lipid/water mixtures. The thermotropically induced L alpha----HII phase transition of the lipid DOPE is used to obtain macroscopically aligned samples in the hexagonal HII phase at 45 degrees C from samples prepared in the lamellar L alpha phase at 7 degrees C. The interpretation of angle-resolved fluorescence depolarization experiments on these phases, within the framework of the rotational diffusion model, yields the order parameters (P2) and (P4), and the diffusion constants for the reorientational motions. The reorientational motion rates of the TMA-DPH molecules in the hexagonal HII phase are comparable with those in the lamellar L alpha phase. Furthermore, the lateral diffusion of the probe molecule on the surface of the lipid/water cylinder in the hexagonal phase is found to be considerably slower than the reorientational motion.