The present work deals with a possible ultraviolet and infrared luminescence of the solid substance of the near-Earth objects. In particular, features of the phenomena of photoluminescence and cathodoluminescence of substance of these objects are considered. It is shown that ultraviolet and infrared luminescence of these objects can be revealed by orbital-based instruments. It is demonstrated that detectability of luminescence of Near-Earth Objects opens up the possibilities for determination the physical-chemical properties of their solid substance and finding of the dark small low-albedo bodies, which could approach dangerously closer to the Earth. Equations for Calculation of luminescence intensity of these objects are proposed. Data on the luminescence of the corresponding minerals and the numerical values of the yields of luminescence and albedo, as the conditions for the detectability of the luminescence of Near-Earth Objects are presented as well.