The effects of minor alloying addition of Cu on the glass-forming ability and crystallization process of Fe 71.7−x B 16.7 Si 8.3 Zr 3.3 Cu x and Fe 72.5−x B 16.7 Si 8.3 Hf 2.5 Cu x (x = 0, 0.3, 0.7, 1.0 and 1.3; at%) alloys were investigated. It was found that the critical glass formation size of rod samples gradually decreased from 2.5 to 1 mm with increasing Cu content in these alloys. Single α -Fe phase nanocrystalline alloys were obtained after isothermal annealing the Fe–B–Si–Zr/Hf–Cu glassy alloys containing 0.7–1.0 at% Cu. The Fe 71 B 16.7 Si 8.3 Zr 3.3 Cu 0.7 alloy exhibited good soft magnetic properties with a high saturation magnetization (~ 1.22 T) and a low coercive force (~ 0.6 A/m) after annealing at 853 K for 10 min due to the precipitation of α -Fe nanoparticles of 8 nm size in the glassy matrix. The structural evolution on annealing and the variation tendencies against Cu content of the glass transition temperature, thermal stability and glass-forming ability of the Fe–B–Si–Zr/Hf–Cu amorphous alloys were discussed using a dual-cluster local structure model. Graphic Abstract