An extreme-ultraviolet (EUV) source based on a low-pressure discharge sustained in a magnetic trap by the high-power millimeter-wave radiation under electron-cyclotron-resonance (ECR) conditions is discussed. Multiple charged ions are efficiently generated and excited in such a discharge (tin ions injected into the trap from a vacuum-arc discharge were used) and emit line radiation in the desired wavelength range. A radiation power of 50 W into a solid angle of in a wavelength range of and an efficiency of about 1% for the conversion of the microwave radiation absorbed in the plasma to the extreme ultraviolet radiation were achieved in the preliminary experiments. The article describes in detail the method of measuring EUV light emission power and background radiation. The emissivity of the plasma heated by gyrotron radiation with frequencies of 170 and 300 GHz is calculated. The proposed scheme can reduce the size of the emitting region up to . The source can operate in both continuous and in pulsed mode.