The effect of domain wall stabilization and their nonuniform movement during magnetization reversal on the frequency dependence of magnetic losses per cycle was studied. Conventional annealing, magnetic annealing, laser treatment, and applying insulating coatings on the surface of ribbons of amorphous alloys with zero and nonzero saturation magnetostriction were used to produce different conditions and degrees of stabilization of domain walls. It is shown that processes favoring the nonuniform jump-like movement of domain walls lead to the formation of (or increase in) the anomaly of the frequency dependence of magnetic losses per cycle during magnetization reversal. These processes are the partial crystallization of alloy, an increase in the volume of domain with the magnetization normal to the ribbon plane, an increase in the magnetoelastic energy, etc.