Two pieces of Fe73.5 Cu1 Nb3 Si13.5 B9 amorphous wires were submitted to thermal treatment without (S1) or under (S2) applied tensile stress, so inducing nanocrystalline structure characterized by two different types of magnetic anisotropy. Sample S1 exhibits longitudinal domain structure with small anisotropy constant, while a transverse domain structure with large transverse anisotropy is induced by stress annealing for sample S2. The specific magnetoimpedance response of each nanocrystalline wire has been studied as a function of the applied torsion, ξ. Both samples show the giant magnetoimpedance (GMI) effect, with GMI ratios of 190% and 145% at ξ=0 for wires S1 and S2, respectively. Applied torsion modifies the form as well as the amplitude of magnetoimpedance, which is discussed in terms of the competition between the magnetoelastic anisotropy induced by the processing and the helical anisotropy induced by the torsion. The torsion impedance has been modeled for the case of sample S1 under large enough helical anisotropy. The observed giant torsion-impedance effect of 320% and 235% for samples S1 and S2, respectively, is proposed to be employed in magnetoelastic torsion sensors. The use of the GMI effect is further emphasized to be a powerful tool to explore the magnetic structure and the magnetic anisotropy. © 2003 American Institute of Physics.