We report the results of new grazing incidence X-ray diffraction studies of Langmuir monolayers of F(CF2)11COOH and F(CF2)10CH2COOH supported on water ; in each case the locations and intensities of the first three diffraction peaks ((1, 0), (1, 1) and (2, 0)) have been measured. These new data are consistent with earlier ones in that both monolayers have simple hexagonal packing of molecules with their long axes nearly perpendicular to the water surface at maximum surface densities. By comparing the ratios of the intensities of the several diffraction peaks observed in each case, one can conclude that at least one of the molecules is not in a free rotator phase. These ratios are used, together with a fit to the Debye-Waller factor, to discriminate between different models of the azimuthal ordering in the monolayer. A model of close packed monolayer with freely rotating molecules is inconsistent with the integrated diffraction intensities for F (CF2)11COOH. Much better agreement is obtained when an orientational ordering of the long axes of the amphiphilic molecules is assumed in the monolayer. On the other hand, in the case of F(CF2)10CH2COOH, either of the two models, free rotating or azimuthal ordering, appears to be equally consistent with the diffraction data.