Nonmagnetostrictive CoFeSiB alloy wires were subjected to cold drawing processing followed by annealing under tension, in order to induce the formation of circular magnetic anisotropy. The axial (MZ–HZ) and circular (MΦ–HΦ) hysteresis loops indicate the existence of induced transverse anisotropy, with the magnitude of the anisotropy field being dependent on the processing conditions, while circular loops are quasibistable for samples processed under stress. Very peculiar hysteresis loops are obtained for the Matteucci (MI, MΦ–HZ) and inverse Wiedemann (IWE, MZ–HΦ) effects corresponding to those samples exhibiting the mentioned circular bistability. The circular shape of the MI loop is interpreted as produced by reversible magnetization rotation within circumferential domain. The effective hysteresis arises from the existence of a helical distribution of anisotropy in the transition region between the inner axial domain and the external shell. IWE loop confirms the presence of this helicity. © 1999 American Institute of Physics.