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Intrinsic electromagnetic oscillations were investigated in layered superconductors of finite dimensions, filling a rectangular resonator. Spectra of both ordinary and extraordinary eigenmodes were obtained. A nonlinear effect of decreasing eigenfrequencies of extraordinary modes was analyzed and generation of the third harmonic of oscillations was studied. A nonlinearity of the system is related to a nonlinear dependence of the Josephson current density across superconducting layers on interlayer phase difference of the order parameter. Josephson plasma waves running along a waveguide filled with a layered superconductor were investigated as well as nonlinear effects appearing during propagations of these waves. In addition, in the work, an effect of the slowing down of terahertz waves in waveguides, which is caused by a mutual effect of nonlinearity and damping of waves is predicted.

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