X-ray diffraction in reflection geometry was used to investigate the influence of the Free surface on the structure of the hexagonal (H-1) phase and the transition temperature from the hexagonal to the isotropic (L-1) phase of the binary nonionic surfactant system penta(ethyleneoxide)-mono-n-dodecyl ether, For four specimens with different surfactant content it was found that the isotropization temperature is shifted toward higher values in a layer close to the surface and that the lattice constant of the H-1 phase in this layer is smaller than the corresponding bulk value, i.e., the coexistence line of thr hexagonal and the isotropic phase is shifted to higher values of surfactant volume fraction in a layer close to the sample surface. From X-ray reflection measurements the thickness of this layer was determined to be about 60 lattice constants.