Oxaliplatin and cisplatin belong to the class of platinum-based anticancer agents. Formation of DNA adducts by these complexes and the consequences for its structure and function, is the mechanistic paradigm by which these drugs exert their antitumor activity. We show that employing short oligonucleotide duplexes containing single, site-specific 1,3-intrastrand cross-links of oxaliplatin, its enantiomeric analogue, or cisplatin and by using gel electrophoresis that under physiological conditions the coordination bonds between platinum and the N7 position of guanine residues involved in the cross-links of the Pt(II) complexes can be cleaved. This cleavage may lead to linkage isomerization reactions between these metallodrugs and double-helical DNA. For instance, approximately 25 % 1,3-intrastrand cross-links of the platinum complexes isomerized after 192 h (at 310 K in 200 mM NaClO4). Differential scanning calorimetry of duplexes containing single, site-specific cross-links of oxaliplatin, its enantiomeric analogue, and cisplatin reveals that one of the driving forces that leads to the lability of DNA cross-links of these metallodrugs is a difference between the thermodynamic destabilization induced by the cross-link and by the adduct into which it could isomerize. The rearrangements may proceed in the way that cross-links originally formed in one strand of the DNA can spontaneously translocate from one DNA strand to its complementary counterpart, which may evoke walking of the platinum complex on DNA molecule. In addition, the differences in the kinetics of the rearrangement reactions and the thermodynamic destabilization of DNA observed for adducts of oxaliplatin and its enantiomeric analogue confirm that the chirality at the carrier 1,2-diaminocyclohexane ligand can considerably affect structural and other physical properties of DNA adducts and consequently their biological effects. In aggregate, interesting generalization of the results described in this work might be that the migration of oxaliplatin, its enantiomeric analogue, or cisplatin from one strand to another in double-helical DNA controlled by energetic signatures of these agents might contribute to a better understanding of their cytotoxic and mutagenic potential.