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We report studies of the magnetic critical behavior as a function of anisotropy strength in rare-earth-rich glasses. Anisotropy is induced in Gd-Co by alloying with Tb. The system studied is Gd65-xTbxCo35 and the random magnetic anisotropy (RMA) strength may be increased by increasing x. The x=0 alloy of this series has been shown to exhibit standard critical behavior expected for a second-order phase transition. With increasing x we find deviations from this behavior due to the presence of RMA. We present detailed results for the alloy with composition x=50 at. % and show that for large enough magnetic fields the system continues to show standard ferromagnetic scaling but for low enough fields the system crosses over to a behavior describable by nonlinear scaling similar to that found in spin-glass systems. Journal of Applied Physics is copyrighted by The American Institute of Physics.