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The fine structure of the experimental secondary electron emission spectra (SEES) along the normal to a Ir(111) surface and the target (total) current spectra (TCS) along the normal to a Cu(111) surface are interpreted theoretically. It is shown that the fine structure of SEES and TCS is mainly due to the electronic structure of unoccupied high-level electronic states (above the vacuum level E vac ) to which the electrons come or from which they emit. The predominant role of the effects of bulk energy-band structure in the formation of spectra is shown. Comparison to existing experimental data is given.