First observation of excitation of surface electromagnetic waves (SEW) is reported in the reststrahlen region in for biaxial crystal KTiOPO4 (KTP) using a tunable CO2 laser around 10 µm, and for CaF2, BaF2, MgO (cubic crystals), and LiNbO3 (uniaxial crystal) in the far IR using ith a free-electron laser. The parameters of SEW propagation in these crystals have been obtained by the interference method of SEW phase spectroscopy, and the possibility of determining the complex dielectric permittivity of crystals from the SEW propagation parameters demonstrated in the range of SEW existence.