A low-frequency model of the magnetization reversal of a microwire is developed for those cases when the microwire magnetization response can go beyond the linear approximation. The analysis of the influence of external magnetic fields on the process of magnetization reversal of the microwire, including the hysteresis mode, was performed. The characteristic dependences of the amplitude of the electromotive force, U2f
, arising in the pick-up coil wound around the microwire are obtained. It was established that, in the region of relatively small-acting circular and longitudinal magnetic fields, the U2f
signal could have a region with the opposite sign. An extended small-angle magnetization rotation method was used to verify the proposed model and test glass-coated, amorphous, Co-rich microwires. During the experiments, the amplitude of the second harmonic, U2f
, arising in the pick-up coil when an alternating electric current with the frequency f
flows through the microwire, was measured as a function of the applied longitudinal magnetic field at various mechanical tensile stresses. The effective anisotropy field, the magnetostriction constant, and the residual quenching stress of the investigated microwires were determined by comparing the theoretical and experimental data.