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Magnetic-susceptibility and high-field magnetization measurements are presented for amorphous Zr40Cu600-xMx (M denoting Gd and Tb), with x ranging from zero to ten. Effective moments of magnetic solutes were determined by fitting susceptibility data to the Curie-Weiss expression. The moments of Gd and Tb are very close to those expected for trivalent ions and the paramagnetic Weiss temperatures are positive. Saturation did not occur in any of the samples, even at 80 kOe and 1.3 K; however, the alloys containing Gd approached normalized magnetization values of unity. High-field hysteresis loops were used to obtain the temperature dependence of the coercive fields Hc and to determine ordering temperatures, defined as those temperatures for which Hc vanishes. The zero-field susceptibility for both the Gd and Tb alloys shows sharp peaks at low temperatures. The magnetically ordered state of the Gd alloys is characterized as spin-glass-like; that is, the spins are frozen in random directions and there are both ferromagnetic and antiferromagnetic exchange interactions, with the former dominant. The Tb alloys also have low-temperature magnetic states characterized as spin-glass-like in this sense. However, in the Tb alloys, the presence of local random anisotropy affects the high-field magnetization considerably. Attempts to fit the high-field magnetization of the Tb alloys to the local-random-anisotropy theory of Harris et al. are described.