The soft magnetic properties of the nanocrystalline Fe–M–B (M=Zr,Nb) alloys, which exhibit a high saturation flux density(Bs)above 1.5 T as well as a high effective permeability(&mgr;e)above 30 000 at 1 kHz, were found to be improved by adding small amounts of Cu and by optimizing the chemical composition. The addition of Cu to the alloys decreases the bcc grain size. The excellent soft magnetic properties (a high&mgr;eof 100 000 at 1 kHz combined with a highBsof 1.53 T) can be achieved in the region where small grain size, as well as nearly zero-magnetostriction are obtained, which is attained in the compositional range aroundFe84Nb3.5Zr3.5B8Cu1.The soft magnetic properties can be further improved by low temperature annealing before the crystallization treatment, probably as a result of a decreased grain size distribution in the crystallized state. Consequently, the&mgr;ereaches the maximum value of 120 000 for the nanocrystallineFe84Nb3.5Zr3.5B8Cu1alloy. ©1997 American Institute of Physics.