The composites and thin films comprising individual single-walled carbon nanotubes with a polymer coating (p-cnts) have been prepared and their electromagnetic responses have been studied in a wide range from low-frequency (25-10 7 Hz) up to the infrared region. In spite of the high volume fraction of the nanotubes (up to 3.3%), the polymer coating prevents direct p-CNT contacts and the formation of the percolation network in those composites, so that p-CNTs interact only via the electromagnetic coupling. thereby it is an ideal model system to verify experimentally the fundamental issues related to carbon nanotube electromagnetics, such as the influence of inter-tube electron tunneling on the localized plasmon resonance in the terahertz range, or the infrared absorption enhancement of polymer molecules attached to the nanotube surface. Along with addressing the fundamentals, applied carbon nanotube electromagnetics got insights important for the applications of p-cnt based composites as dielectric media in the terahertz regime. In particular, we found that the real part of the permittivity of the p-CNT film in the terahertz range is rather competitive, i.e. 8-13, however the loss tangent is not so small (0.4-0.6) as has been predicted. The way to increase p-CNT terahertz performance is also discussed. Among carbon nanoparticles, metallic single-walled carbon nanotubes (CNTs) have a huge aspect ratio (10 2-10 7) and high conductivity that both provide their strong interaction with the electromagnetic and optical radiations 1-4. The high kinetic inductance of a single-walled CNT causes the slowed-down surface wave propagation along the tube in the range of the intraband electron transitions (<40 THz) 5,6. The excitation of the standing surface waves by a plane wave manifests itself as antenna resonances in the polarizability spectrum of an individual finite-length CNT 3. The first antenna resonance also called as localized plasmon resonance (LPR) appears as a broad terahertz peak in the conductivity spectra of the CNT films 7-9. The scattering theory has been developed for individual and bundled CNTs 3,10 , curved CNT 11 , CNT with a mesoscopic insertion 12 and dielectric coating 13. The electromagnetic response of a CNT composite has been theoretically described from radio-frequency up to the visible range with the Waterman-Truell approach 8 that is valid for non-interacting inclusions, i.e. when the electromagnetic interaction and electron tunneling coupling between the tubes are small. However, theoretical study of the mutual impedance between two carbon nanotubes 14,15 in radiofrequency and microwave ranges shows that the electromagnetic interaction between CNTs is essential if the distance between them is less than 0.02λ 15 (λ is a wavelength of the electromagnetic wave in the surrounding