Wines aged in oak wood barrels with various uniform tannin contents (which were classified according to their total ellagitannins contents as predicted by Near Infrared Spectroscopy on the untoasted wood) and different toasting levels (high precision toasting by radiation) were distinguished according to their overall abilities to resist against oxidation. Wine trials were carried out on two different vintages (2015, 2016) and three grape varieties (Sauvignon blanc, Semillon, Chardonnay). Regardless of the vintage and the wine matrix, a relationship was established between wine oxidative stability (based on EPR spin trapping methodology) and oak barrel tannin potential. The extraction kinetic of ellagitannins by wines appeared linear during barrel aging and achieved its maximum at six or eight months, in a grape variety dependent manner. Oak wood barrel tannin potentials and toastings had no effect on wine glutathione and polyphenols contents. However, wines aged in new barrels with both low and medium tannin potentials, preserved at the end of aging and important number of S-N containing compounds, which was in addition to the known ellagitanins, revealed wines better antioxidant stability.