The effect of processes such as domain-wall movement and magnetization rotation and factors such as the magnetoelastic energy, magnetostriction, and the type of moving domain walls on the anomaly in the frequency dependence of magnetic losses per cycle of magnetization reversal was studied. The domination of the processes and factors in soft magnetic alloys with zero and nonzero saturation magnetostriction is achieved by annealing with and without a magnetic field. It is shown that magnetization rotation and movement of 180° domain walls do not lead to the formation of an anomaly in the frequency dependence of magnetic losses, whereas the processes that increase the nonuniform jumplike movement of domain walls favor the formation of the anomaly.