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Background: Coumarin derivatives possess a wide range of biological activities. By functionalization of the parent coumarin skeleton that has neither antioxidant nor biological activity, a series of new bio-antioxidants has been designed., Results: New antioxidant compositions (equimolar binary and ternary mixtures) of eight 4-methylcoumarins and three related compounds have been tested and different effects between individual components have been observed: synergism (positive effect), additivism (summary effect) and antagonism (negative effect). Higher oxidative stability of the lipid substrate was obtained in the presence of the new antioxidant compositions of the studied compounds with dl-α-tocopherol and l-ascorbic acid. The role of each component in the antioxidant compositions of ternary mixtures has been identified by using new equations composed by the authors., Conclusion: All ternary mixtures demonstrate synergism as a result of continuous regeneration of dl-α-tocopherol from the studied antioxidants and l-ascorbic acid. Theoretical calculations have been probed as indicators of the expected effects between the individual components in a binary mixture. © 2018 Society of Chemical Industry., (© 2018 Society of Chemical Industry.)