Oxidative stress is considered to act as a universal physiological constraint in life-history evolution of animals. This should be of interest for extra-pair paternity behaviour, and we tested here the prediction that offspring arising from extra-pair matings of female great tits show higher resistance to oxidative stress than within-pair offspring. Resistance to oxidative stress, measured as the whole blood resistance to a controlled free-radical attack, was significantly higher for extra-pair offspring as predicted although these were not heavier or in better body condition than within-pair offspring. Since resistance to oxidative stress has been suggested to enhance survival and reproductive rates, extra-pair offspring with superior resistance to oxidative stress, be it through maternal effects or paternal inheritance, may achieve higher fitness and thus provide significant indirect fitness benefits to their mothers. In addition, because oxidative stress affects colour signals and sperm traits, females may also gain fitness benefits by producing sons that are more attractive (sexy-sons hypothesis) and have sperm of superior quality (sexy-sperm hypothesis). Heritability of resistance to oxidative stress as well as maternal effects may both act as proximate mechanisms for the observed result. Disentangling these two mechanisms would require an experimental approach. Future long-term studies should also aim at experimentally testing whether higher resistance to oxidative stress of EP nestlings indeed translates into fitness benefits to females.