A comparative study of LiNbO3 single crystals with congruent and near-stoichiometric compositions was performed using hyperfine interactions and ion beam techniques. Our data show that the structure of congruent LiNb03 cannot be completely dcscribed by the models which assume only vacancies and Nb antisites. Additional disorder has to be considered both at the Li and Nb sites. The additional defects are cation stacking inversions, in which the cation sequence coincides locally with the one of ilmenite-like LiNb03. We suggest that these stacking inversions are associated with the Nb antisites necessary for charge compensation in Li-deficient material.