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 epsilon at the frequencies in the tuning range of a free electron laser (FEL) without any preliminary epsilon 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 CaF 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.