Abstract: Method for producing soft magnetic alloys with very high permeability, in which an ingot is cast containing in its composition more than 70% nickel or more than 45% cobalt, the metal having, or not having, been subjected to a secondary metallurgical step, the ingot is remelted under an electroconductive slag, the remelted ingots being converted into strips after hot rolling then cold rolling, the strips then being subjected to a treatment for developing magnetic characteristics, in which method the alloy is remelted under an electroconductive slag comprising at least the first three components of the system: CaF.sub.2, CaO, SiO.sub.2, Al.sub.2 O.sub.3, and defining a zone in a ternary diagram delimited by the following proportions by weight:CaF.sub.2 (50-75)%CaO (20-30)%SiO.sub.2 (5-15)%with Al.sub.2 O.sub.3 <3%.