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We present the results of attenuation measurements in water-equivalent material of high energy photon beams at off-axis points. The measurements were performed on four accelerators and for the energies of 4, 6, 12, 15 and 23 MV in narrow beam geometry with and without flattening filter. We found a linear increase of the attenuation coefficient as a function of the distance from the central axis for all the energies and types of linear accelerators. For the same nominal energy, this increase is different from one accelerator to another. The same phenomenon was observed for the attenuation coefficients obtained without flattening filter in the same experiment conditions. These results are tentatively interpreted considering the angular variation of bremsstrahlung energy spectra with and without flattening filter as calculated by a Monte-Carlo method.