The model for the influence of surface fields H p generated by the core current has been employed for the investigation of the magnetization processes and the domain structure in an initially amorphous Fe 7 3 . 5 Cu 1 Nb 3 Si 1 5 . 5 B 7 ribbon which was successively annealed at selected temperatures T a up to 540°C. The analysis of the dM/dt vs. H curves and the M-H loops showed that in the as-received state only a fraction of inner domains with magnetizations I nearly parallel with the ribbon axis (i.e. with small angles δ between I and ribbon axis) participate in magnetization process. The analysis of the effects of H p on the coercive field H c and the shift of the center C of the M-H loop shows that the annealing up to T a = 450°C reduces the average strength of pinning S u of the domain walls whereas the angle δ changes only a little with T a . For T a ≥ 400°C the maximum magnetization M m practically reaches the saturation magnetization M s ( 1.3 T) already in the magnetizing field H 0 =100 A m - 1 which indicates rather simple domain structure with I mostly along the ribbon axis. At T a = 450°C H c reached its minimum value, probably associated with the formation of nano-sized Fe-Si particles. Further annealing (T a > 450°C) leads to rapid increase in both S u and δ , hence also in H c , as already observed in the previous studies.