The stress-dependent AC magnetisation, remanence and susceptibility of three as-quenched and annealed amorphous wires have been studied. Instead of any minor loop at low field, high-magnetostrictive wires show a large Barkhausen jump when the applied field exceeds a critical value. The dependence of this critical value on stress has also been studied. The results have been interpreted by taking into account the unique distribution of internal stresses which produces two distinct radial and axial anisotropy regions in high-magnetostrictive wires. These two distinct regions are absent in low-magnetostrictive wires and hence their behaviour is similar to that of amorphous ribbons. © 1990 IOP Publication Ltd.