An analysis of electrodynamic properties of high-temperature superconductors with the AC magnetic field parallel to the layers is presented. The system is modelled as a superlattice of normal (N) and superconducting (S) layers, and the bulk superconductivity is maintained by the proximity effect. The expression for the system conductivity is evaluated. The AC losses in the region of frequencies Ω smaller than 2∆ (∆ is the order parameter value at zero temperature) are non-zero even at T = 0; several peaks on the frequency dependence of the conductivity are predicted. Comparison of this result with experimental data is discussed.