We have observed that LiNbO3:Mg (0.19-5.91 mol % MgO) crystals experience rearrangements in their defect structure with increasing concentration of Mg and exhibit optical anomalies related with them, which have a threshold character. We have shown that, at Mg concentrations close to the first concentration threshold at similar to 3.0 mol % MgO, the optical homogeneity of the crystals increases. When the Mg concentration approaches the second concentration threshold, we have revealed a significant shift (by similar to 50 cm(-1) compared to that in other crystals) of the entire IR absorption spectrum in the range of stretching vibrations of OH groups to the high-frequency range, a sharp decrease in the number of protons, and a jumpwise shift of the absorption edge in the short-wavelength range. We have shown that the shift occurs because all Nb-Li point defects are replaced by Mg cations near the concentration threshold at 5.5 mol % MgO, and, subsequently, Mg cations occupy only positions of Li and Nb cations of an ideal stoichiometric structure, forming Mg-Li and Mg-Nb point defects.