We use small-angle X-ray scattering to investigate the structures under she
ar of surfactant hexagonal phases swollen with oil. Rheology studies of the
se materials indicate a shear-induced transition between two states of diff
erent viscosity. In the low shear regime, the cylinders are preferentially
oriented along the flow and the hexagonal phase exhibits a polycrystalline
texture. Unexpectedly, a high shear has the effect of melting the long-rang
e two-dimensional (2D) order of the cylinders, leading to a 2D liquid of cy
linders strongly aligned along the flow.