X-ray emission ranging 0.5 - 10.0 keV with the dose power rate up to 0.01 J/s emanating from the cathode solid in the high-current Glow Discharge has been registered in earlier experiments. The X-rays were recorded during the Glow Discharge operation and after the Glow Discharge current switch off. Presumably the observed X-ray emission proceeds as a result of relaxation of excited energetic levels in the cathode solid medium. These excited levels are formed during the exposure of the cathode sample solid surface to the effect of the ions flux produced by plasma or electrolyte medium. The energetic and temporal characteristics of the X-ray emission have been studied with reference to the cathode material used, the kind of plasma-forming gas and the Glow Discharge operational parameters. The experiments were carried out on the high-current Glow Discharge device in D2, H2, Kr and Xe at pressure up to 10 Torr, current up to 200 mA, and the Glow Discharge voltage ranging 500-2500 V, the cathode samples being made of Al, Sc, Ti, Ni, Nb, Zr, Mo, Pd, Ta, W, Pt.. The registration of X-ray emission was performed using Al2O3-based TLD (thermo-luminescent detectors), the obscure chamber with the objective of 0.3 mm-diameter (the X-ray emission being recorded onto X-ray film and nuclear emulsion), and PM scintillating detectors for the recording of temporal characteristics. All the detectors were covered with a protective 15μ m- thick Be shield. The X-ray spectra were registered on a film with the curved mica crystal X-ray spectrometer. The X-ray emission spectrum from the Pd cathode consists of spectral bands with energies ranging 0.81 - 0.84 keV, 1.3 - 1.5 keV, 2.5 - 2.9 keV. The Excess Heat power was registered in experiments with high-current Glow Discharge and High-Voltage Electrolysis (up to 1000 V ) proceeding from the assumption that certain excited energetic states (0.5 - 10.0 keV) formed in the cathode solid medium trigger LENR (Low Energy Nuclear Reactions) which leads to production of Excess Heat power and nuclear ash. The experiments showed that the maximum Excess Heat power values of 5 -15 W for Glow Discharge and 180-280 W for High-Voltage Electrolysis, and Efficiency up to 160% for Glow Discharge, and 800% for High-Voltage Electrolysis, respectively, were registered at the anode/cathode voltage ranging 1000-1300 V This may be achieved by devising a mechanism for conversion of 0.5 - 3.0 keV plasma ions flux initial energy into 0.5 - 10.0 keV high-energetic excitation of a solid nuclear electronic system. Presumably such a conversion takes place in the cathode sample solid exposed to bombardment by the discharge plasma ions. This process is evidenced by intensive X-ray emission recorded during the Glow Discharge operation and after the Glow Discharge current switch off. The energetic and temporal characteristics of the X-rays are determined by the energy and lifetime of the excited energetic levels in the cathode solid medium.