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This paper presents an analysis of eddy-current losses in magnetic conductors with abrupt magnetic transitions. The study of the linear polarization of the magnetic flux is based on the Preisach model representation of eddy-current hysteresis. By using this representation, analytical formulas for the calculation of eddy-current losses in terms of simple experimental data are derived. The analysis of the circular polarization of the magnetic flux is carried out through the exact analytical solution of the corresponding nonlinear vector diffusion equation. It is shown that the f2 law for eddy-current losses has a universal character.