- AC losses in superconducting wires and tapes are usually studied for applied sinusoidal currents and/or magnetic fields. However, currents in electric power systems contain a variety of harmonics. We solved analytically and numerically, in the infinitely thin approximation, the transport current and magnetization problems for coated conductors under non-sinusoidal conditions. The analytical expressions for eddy current and hysteresis losses have been obtained in the framework of the critical state model neglecting the response of the normal-metal substrate and stabilization layers. The contribution of higher harmonics to losses per cycle is determined by both their phase shift relative to the main harmonic and their amplitude. It has been shown that the 5% third current harmonic (for the phase shift ?) increases eddy losses in the normal-metal parts by up to 90% at a transport current close to the critical value.Numerically, for the power law current?voltage characteristic of a superconductor, the contribution of higher harmonics to the total losses in a coated conductor was investigated in a wide range of the power index. It has been shown that even at a low power index (n?=?4) this contribution can achieve 44% of losses caused by the main harmonic only. For high external magnetic fields an approximate analytical solution has also been derived and compared to the numerical solution.