It is shown that Be2+ and Ca2+ impurity ions in wide-gap (E-g = 7,8 eV) MgO: Be and MgO: Ca single crystals serve as the traps for highly mobile holes, which do not undergo self-trapping in the bulk of MgO. Recombination of conduction electrons with trapped-hole centres in MgO: Be and MgO: Ca at 10 K causes the appearance of broadband luminescence (peaked at 7.2 and 6.8 eV) the thermal quenching of which occurs at 190 or 50 K, respectively. The peaks of thermally stimulated luminescence connected with the recombination of mobile holes, thermally released from trapped-hole centres, with the electrons still localized nearby defects have been detected in the samples previously irradiated by 5-10-keV electrons or 25-eV photons. [Be](+). [Ca](+) trapped-hole centres are charged ones (Coulomb centres) and have a large cross-section for the nonradiative recombination with hot conduction electrons. Such hot recombination can be considered as one of the creation mechanisms of Frenkel defects in the materials, where the formation energy of a Frenkel pair exceed E-g.