Spectra of metastable optical absorption and its relaxation kinetics have been studied in zinc-doped BeO crystals by time-resolved pulsed absorption spectroscopy. A comparison of the observed induced optical absorption of self-trapped excitons and small-radius excitons bound to the zinc impurity suggests that their hole components have similar structures and reveals distinctive features of "forbidden" optical transitions in the electronic components. Metastable optical absorption in Zn+ centers has been discovered. It is shown that the small-radius excitons bound to the zinc impurity form in the hole stages of thermally stimulated tunneling recombination processes involving Zn+ electronic centers. It has been found that the high recombination probability of the electronic and hole centers created in BeO-Zn crystals by an electron beam may be due to the high degree of their spatial correlation.