Despite significant achievements in the elucidation of the nature of protein-DNA contacts that control the specificity of nucleotide incision repair (NIR) by apurinic/apyrimidinic (AP) endonucleases, the question on how a given nucleotide is accommodated by the active site of the enzyme remains unanswered. Therefore, the main purpose of our study was to compare kinetics of conformational changes of three homologous APE1-like endonucleases (insect Drosophila melanogaster Rrp1, amphibian Xenopus laevis xAPE1, and fish Danio rerio zAPE1) during their interaction with various damaged DNA substrates, i.e., DNA containing an F-site (an uncleavable by DNA-glycosylases analog of an AP-site), 1,N6-ethenoadenosine (εA), 5,6-dihydrouridine (DHU), uridine (U), or the α-anomer of adenosine (αA). Pre-steady-state analysis of fluorescence time courses obtained for the interaction of the APE1-like enzymes with DNA substrates containing various lesions allowed us to outline a model of substrate recognition by this class of enzymes. It was found that the differences in rates of DNA substrates’ binding do not lead to significant differences in the cleavage efficiency of DNA containing a damaged base. The results suggest that the formation of enzyme–substrate complexes is not the key factor that limits enzyme turnover; the mechanisms of damage recognition and cleavage efficacy are related to fine conformational tuning inside the active site.