[en] It is shown that the strong reduction of the magnetic losses observed in nanocrystalline alloys after transverse field annealing is chiefly related to an abnormally slow increase of the excess loss component with the magnetizing frequency. Eddy current counterfields tend to hinder the domain wall processes to a larger extent than spin rotations, progressively inhibiting the related loss mechanisms at increasing frequencies. This results in a reduced role by the excess and hysteresis loss components, which can be assessed by suitable generalization of the statistical theory of losses