||Giant magneto-impedance (GMI) effects were studied in crystalline Mumetal(Ni73.35Fe13.56CU6.57 Mo5.64Mn0.88), HYMU80 (Ni80.00Fe14.93Mo4.20Mn0.5O SiO.35CO.02) and glassed-covered amorphous wires (Co75Si10B5 and Co68 Mn7Si10B15). The GMI data were obtained from two types of quasi-static scans: (1) magnetic field scan (-115.5 Oe ≤ H ≤ 115.5 Oe) at fixed frequencies, and (2) frequency scan (20 Hz ≤ f [less than or equal to][less than or equal to] 30 MHz) in either zero field or saturating field Hs. The frequency and thickness dependencies of the giant magneto-impedance (GMI) can be explained as due to a combination of high magnetic permeability and the domain wall motion. Effects of annealing on the GMI properties were investigated. For Mumetal, the maximum MI sensitivity \d(δZ/Z)/dH\max was 1.8 %/Oe in the as-cast state, and increased by a factor of 10 to about 21 %/Oe after annealing at T=580° C. We suggest that the enhanced GMI in Mumetal upon annealing at 580 ° C is due to the removal of stresses that accumulate in the process of the metal sheet manufacturing. Annealing at higher temperatures leads to recrystallization and decrease of the GMI effect. The maximum sensitivity obtained in amorphous Co68 Mn7Si10B15 wire was as large as 66 %/Oe. After ac current annealing of amorphous wires, the sensitivity of the GMI effect is also enhanced. The obtained values of GMI sensitivity are two orders of magnitude larger than those of giant magnetoresistive materials. Therefore, the GMI effect offers a potential basis for application in a relatively simple, very high sensitivity magnetic field sensor, which can be used in read-heads.