Electrodeless discharges in high-frequency electromagnetic fields were investigated in conditions where the ratio of linear dimensionlof the discharge space to the electromagnetic wavelength λ in air was 10−3<l/λ<10−1, at frequencies between 106and 108c/s. The power introduced into the discharge space varied from fractions of watts to 100 kW, and the electric field strength was varied between tens and hundreds of volts per cm. There are two different types of discharge: “E-discharges,” in which the elementary conductance currents are continued by dielectric currents, and “H-discharges,” with elementary conductance currents in the form of closed curves.When the ratiol/λ is less than 10−1 then the electrodeless discharges in air at atmospheric pressure may exist at distances of the order of centimetres from the current-carrying electrodes. Further development of the ultra-high-frequency technique leads to constructions of electromagnetic radiators in which the dimensionlis greater than the wavelength λ. With such radiators it is possible to have high concentration of electromagnetic energy at distancesxup tol2/λ which may be some metres or perhaps kilometres from the electromagnetic radiator. When 1 ≫ λ andl2≫xλ it is possible for a natural breakdown to occur in an electromagnetic ray.