Asymmetrical giant magneto-impedance (AGMI) in Co-based amorphous wires with a circumferential anisotropy, which utilises a high frequency axial bias field is proved to be very sensitive to the frequency of excitation and the dc current applied to the wire. The AGMI effect is studied in terms of the surface impedance tensor, demonstrating that the extent of asymmetry is determined by the ratio of the diagonal sigma (zz) and off-diagonal sigma (z phi) components of this tensor.