Detailed investigation of the d M/d t versus H curves and the corresponding M- H loops for as-received magnetostrictive Fe 80B 20 alloy and nonmagnetostrictive Co 70.3Fe 4.7Si 15B 10 alloy carrying direct currents J d ≤ 160 mA has been performed. For both alloys (representing two major classes of amorphous ferromagnetic alloys) the model for the influence of the surface field H p generated by J d correctly describes the motion of domain walls (as evidenced from d M/d t versus H curves) and the variations of the macroscopic parameters such as the coercive field H c and the position of the center of the M-H loop, C with H p can be explained in terms of these motions. Moreover the numerical values of the parameters which govern the magnetization processes at lower H are deduced from these variations. Therefore the model presents a tool for the study (and improvement) of amorphous ribbons. The deviations from the model predictions occurring in Co 70.3Fe 4.7Si 15B 10 alloy at elevated H p are explained in terms of the influence of H p on the domain structure of this alloy.