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An anomalous magnetic behavior has been observed in rare-earch-rich metallic glasses of the composition (R75Au25)100-xBx where R denotes Pr, Gd, Tb, Er and x=0,10. The observed hysteresis in all samples except Gd at liquid-helium temperatures is due to the large anisotropy which develops below the ordering temperature. High-field-magnetization measurements up to 220 kOe were used to determine the spontaneous magnetization and the magnetic anisotropy constant which was found to be of order 108 erg/cm3 for the Tb and Er glasses. These parameters were used together with the observed remanence ratio to examine the high coercive fields in terms of recently proposed models of random anisotropy.