Methods are described of producing regular intense longitudinal electromagnetic waves in vacuum or in plasma which were reported in individual communications from the Kharkov Physico-Technical Institute. Such waves are produced in vacuum if beams are passed through spatially-periodic fields of a parametric resonance region. Slow waves are produced due to the anomalous Doppler effect. When beams are passed through a region containing plasma, a wave with a broad frequency spectrum is formed due to plasmabeam instabilities. Such a wave is regularized by the superposition of a small amplitude periodic signal. Slow waves are produced by subjecting the plasma to an external magnetic field. The possibility is discussed of utilizing the fields so obtained to accelerate ions to high energies.