In this paper we report on measurements of the MI effect in some Co-based commercial ribbons. The impedance of the amorphous ribbons is found to be a very strong function of the drive current frequency. It is also observed that at frequencies higher than 100 kHz, this response becomes sensitive to the application of a dc magnetic field that leads to a maximum value for the MI effect at an applied dc magnetic field higher than the saturation magnetic field of the samples. At frequencies above 100 kHz, the transverse ac field interacts with the longitudinal dc field due to the movement or realignment of the magnetic domains. Thus, the dc magnetic field modifies the ac permeability of the ribbon. Since amorphous ferromagnetic ribbons show nonlinear relationship between the applied dc magnetic field and the magnetic induction, the ac permeability does not change linearly with the applied dc magnetic field. The impedance of the ribbon strongly depends on the coupling of ac field with transverse domains and shows nonlinear relationship with dc magnetic field. It is also observed that the maximum MI ratio varies strongly with the frequency and with the amplitude of the ac drive current.