A nanocrystallised tape-wound core without a localised airgap, consisting of a nanocrystalline material with the following atomic composition: [Fe.sub.1-aNi.sub.a]100-x-y-z-a-.beta.-.gamma.Cu.sub.xSi.sub.yB.sub.zNb.s- ub.aM'.sub..beta.M''.sub..gamma., wherein a.ltoreq.0.3, 0.6.ltoreq.x.ltoreq.1.5, 10.ltoreq.y.ltoreq.17, 5.ltoreq.z.ltoreq.14, 2.ltoreq.a.ltoreq.6, .beta..ltoreq.7, .gamma..ltoreq.8, M' is at least one of the elements V, Cr, Al and Zn, M'' is at least one of the elements C, Ge, P, Ga, Sb, In and Be, with a permeability .mu. of 200 to 4000, a saturation of more than 1T, an induction range, in which the permeability does not vary by more than 5%, of more than 0.9T, a remanent induction of less than 0.02T and a cut-off frequency higher than 1 MHz, such that .mu. varies by less than 1% when the core is aged for 100h at more than 100.degree. C., .mu. varies by less than 5% when the core is coated, .mu. varies by less than 15% when the temperature is in the range of -25.degree. C. and +60.degree. C., and by less than 25% when the temperature is in the range of -40.degree. C. and +120.degree. C., and .mu. varies in a monotonic and substantially linear manner with a temperature of -40.degree. C. to +120.degree. C.