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Results of magnetic measurements are presented on the new metallic glass systems (R80Ga20)100-xFex and (R80Ga20)90B10, where R denotes the heavy rare earths Gd, Tb, and Er, for x=10, 20, and 30, respectively. High-field magnetization (to 80 kOe) and ac and dc susceptibility measurements were made from 1.4 to 300 K. The Gd-Fe glasses are simple ferrimagnets with opposing Gd and Fe moments. The Gd-B glass exhibits two apparent transitions (paramagnetic—ferromagnetic—like, and ferromagnetic spin-glass) as the temperature is lowered. As Fe is added, the low-temperature transition disappears. The data can be understood in terms of Sherrington-Kirkpatrick—type models for the phase diagram with competing ferromagnetic and spin-glass order. In the Tb and Er glasses a strong local random anisotropy prevents saturation of the magnetization in high fields, and the ac susceptibility shows sharp peaks indicating speromagnetic (spin-glass-like) order. In high fields the moment approaches that expected for a hemisphere of randomly oriented spins (1/2gJ/spin), so that an asperomagnetic structure is produced by the applied field. For small values of x (10 and 20), the Tb and Er glasses exhibit coercive force, Hc, and hysteresis characteristics consistent with coherent-rotation processes. However, for large Fe concentrations (x=30), the ac susceptibility peaks are considerably smeared, suggesting increased chemical short-range order and increased heterogeneity. The observed increase of Hc in these alloys seems to be consistent with the theory of Paul, although the choice of parameters is not well defined. The temperature dependence of Hc for the x=30 alloys indicates that domain-wall motion or nucleation processes appear to dominate magnetization reversal.