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The conditions of the existence and transformations of surface electromagnetic waves (SEWs) on metals (surface plasmons) and dielectrics (phonon-polaritons) are discussed. Interferometric SEW experiments provide the possibility for the direct determination of the real and imaginary parts of the dielectric constants at the frequencies in the tuning range of a free electron laser (FEL) without any preliminary models. The important role of the outstanding facilities of FEL—namely, the broad tuning range, high power, narrow bandwidth of emission, and well-collimated beam—in SEW experiments is outlined. It is demonstrated by the examples of the infrared absorption spectra of a Langmuir-Blodgett film on metal, of a metal oxide film, and of polymeric films of nanometer thicknesses on metals. Free surfaces of single-crystal CaF2 and the thin polymeric film were studied by an interferometric experiment for the optical constant determination. Nonlinear spectroscopic applications of the SEW-FEL technique to studies of a second harmonic generation (SHG)—the frequency dependence of efficiency, the angle dependence of SHG, and the influence of a thin-film deposition on a quartz surface—are described.