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The effect of hydrogen on magnetic properties of metallic glasses of the form (R80Ga20)1-xTxHy where R=Pr, Nd, Gd, Tb, Er; T=Cr, Fe, Co, B; 0≤x≤0.3 and 0≤y≤1.7 is reported. The anisotropic rare earth glasses without H all exhibit speromagnetic (spin-glass-like) transitions and the effect of hydrogen, in most cases, is to lower the peak in χac significantly but leave TC relatively unchanged. For the Gd glass with T=Fe and x=0.1 the introduction of H at the level y=0.55 causes a large decrease in TC and a significant increase in local random anisotropy. Models for these phenomena are discussed. Journal of Applied Physics is copyrighted by The American Institute of Physics.