- Study of AC losses in superconducting wires and tapes is usually restricted by consideration of applied sinusoidal currents and/or magnetic fields. However, currents in electric power systems contain a wide variety of harmonics. The currents become strongly non-sinusoidal at the operation of converters, non-linear reactors, and during transient and overload conditions. We report the results of the analysis of the influence of higher harmonics of the current and magnetic field on AC losses in superconducting slabs, strips and coated conductors. Analytical expressions are obtained in the framework of Bean's critical state model; the power law voltage-current characteristics are treated numerically. It is shown that the contribution of higher harmonics to AC losses in superconducting elements can be tens times larger than in normal metals and the 5% harmonic can increases the losses by up to 20%.