Production of a magnetic core of soft magnetic iron-based alloy having a nanocrystalline structure involves determining the annealing temperature (Tm) required, for an amorphous ribbon of the alloy, to achieve maximum magnetic permeability and subjecting a core blank, produced from an amorphous ribbon of the alloy, to annealing at 20-50 (preferably 20-40) degrees C above Tm for 0.1-10 (preferably 0.5-5) hrs. to cause nanocrystal formation. The alloy has the composition (in atomic %) 60% Fe, 0.1-3% (preferably 0.5-1.5) Cu, 0-25% B, 0-30% (preferably 12-17) Si, 0.1-30% (preferably 2-5) one or more of Nb, W, Ta, Zr, Hf, Ti and Mo, and balance impurities, the sum of Si and B being 5-30% (preferably 15-25).
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