We have studied the process of magnetization reversal in amorphous microwires under the action of a longitudinal (axial) high-frequency magnetic field. The amplitudes of harmonics in the frequency spectrum of the response voltage between the wire ends were measured as functions of the high-frequency field amplitude and a dc axial magnetic field strength. For relatively large amplitudes of the high-frequency field, the first several harmonics in the frequency spectrum of the response voltage are highly sensitive with respect to the dc magnetic field. The experimental results are interpreted within the framework of a simple electrodynamic model.