Abstract A numerical simulation model based on Machado et al. [J. Appl. Phys. 79 (1996) 6558] was developed to study the relaxation time and GMI in a series of Co-and Fe-based commercial alloys in the ribbon form as a function of excitation frequency and DC bias field. In Machado et al's model the relaxation time was considered as constant. Based on our experimental observations, we considered the relaxation time as a function of frequency and applied field. In this paper we report on the establishment of a general expression of the relaxation time for both Fe-and Co-based alloys.