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Nonmagnetostrictive Co-rich amorphous wires, 130 μm in diameter, were stress annealed to induce a transverse anisotropy. The resultant structure consists of a circular-magnetization single domain except in a thin core, 2 μm in diameter, where magnetization is axially oriented. The wall interconnecting the outer shell with the core magnetization induces a local helical anisotropy during the annealing. As a consequence, a strong link between the magnetization directions in both regions appears. It is shown that direct current axial fields produce remarkable shifts of the circular hysteresis loops. © 1999 American Institute of Physics.