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We demonstrate the existence of an anomalous structure in the data on the diffractive elastic scattering of hadrons at high energies and small momentum transfer. We analyze five sets of experimental data on p(p)− p scattering from five different experiments with colliding beams, ranging from the first-and second-generation experiments at √ s = 53 GeV to the most recent experiments at 546 GeV and at 1800 GeV. All of the data sets exhibit a localized anomalous structure in momentum transfer. We represent the anomalous behavior by a phenomenological formula. This is based upon the idea that a 1