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ac susceptibility and magnetization measurements are reported for a number of Gd and Tb based glasses. Raman magnetic anisotropy effects are observed in both the Gd and Tb glasses. The Gd glasses show a transition to an infinite susceptibility state and in some cases a further transition to an hysteretic state at low temperatures in which field-cooling and magnetic viscosity effects are observed. The Tb glass shows only a small speromagnetic peak at low temperatures. The ratio of anisotropy strength to exchange was varied in the Gd glasses by alloying, and the effect of this on the resulting magnetic states is discussed. Journal of Applied Physics is copyrighted by The American Institute of Physics.