The effect of external (torsion and tensile) stresses on the electrical impedance of nearly-zero magnetostrictive amorphous microwires (conventional and glass covered) is reported. Glass coated Co 68.5 Mn 6.5 Si 10 B 15 microwire exhibits a maximum relative change in magnetoimpedance ratio up to around 130% at a frequency of 10 MHz, magnetic dc field of about 180 A/m and under tension of 60 MPa. This giant magnetoimpedance (GMI) effect of the microwire is affected by the magnetoelastic anisotropy induced in the sample by applying tensile stress. In addition, from the linear variations of the magnetic field H m corresponding to the maximum DZ/Z ratio, with the applied tensile stress, that is the H m (s) curve, the magnetostriction constant of this amorphous microwire (l s % --2 Â 10 --7 ) is estimated. The torsion giant impedance (TGI) ratio (DZ/Z) x has been investigated in as-cast and annealed (Co 0.94 Fe 0.06 ) 72.5 B 15 Si 12.5 conventional amorphous microwire.As-cast conventional microwire shows a slightly asymmetric Torsion Giant Impedance (TGI) and such asymmetry can be eliminated by current annealing or enhanced by current annealing under torsion. The asymmetry of (DZ/Z) x in the as-cast state and after torsion annealing could be ascribed to the spontaneous or induced helical magnetic anisotropy, which can be compensated by the application of certain torsional stress.