A systematic study of the magnetization processes underpinning the giant magnetoimpedance phenomenon at low frequencies (f < 10 MHz) is presented. Instead of observing only the total impedance as the main parameter, in this paper we make use of the complex permeability formalism, by calculating permeabilities from complex impedance results. We first investigate the effects of the ac magnetic field amplitude (as produced by the ac current flowing through the sample). Results point to domain wall bulging as the dominant magnetization process for low ac field amplitude. As this amplitude increases, domain walls are unpinned and displaced, leading to hysteresis. As frequency increases, a clear relaxation behavior is observed. The effects of the de field are then studied. This parameter produces a damping of domain wall processes, leading to a serious decrease in permeability. Very high frequencies are also considered (f in the GHz range) from results recently published, which lead to a complete image of all the magnetization processes, since these results clearly show spin rotation and resonance. (C) 2001 Elsevier Science B.V. All rights reserved.