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The optical absorption and cathodoluminescence spectra of nine diamond specimens are investigated at the temperatures 295 K and 82–295 K, respectively. By the presence of an N3a electron-vibrational system with a phonon-free line at 2.68 eV, six of them are identified as natural diamonds. By the presence of the electron-vibrational system at 2.56 eV and a structureless band at 2.54 eV, associated with nickel in the optical absorption and luminescence spectra, two specimens are identified as synthetic diamonds grown at high pressures and temperatures. By the presence of exciton luminescence at 5.271 eV and the absence of any spectral, impurity-related peculiarities, one of the specimens is identified as a synthetic diamond grown by the chemical vapor deposition. Based on the data obtained, a procedure is proposed for identifying natural and synthetic diamonds and determining a model scheme of the radiation-thermal treatment of the specimens.