FeBSi-based metallic glasses are known to exhibit high permeability for line frequency excitation. The substitution of 2-3 atom percent of Cr or No for Fe in these glasses decreases saturation magnetization by 0.1-0.2 T/at.% but substantially improves coercivity, permeability, and core loss at low to moderate induction levels. When longitudinally annealed, the substituted alloys exhibit coercivities of 0.3-0.7 A/m and 60 Hz permeabilities of 300,000-400,000, compared with the 1 A/m and 200,000 typical of FeBSi plasses. A transverse anneal of the substituted alloys results in nearly equal permeabilities under either bipolar or unipolar 60 Hz excitation. The improvement in 60 Hz properties is largely due to the decrease in the hysteresis component of loss.