Extra-pair paternity is known to be common in many socially monogamous avian species. One question to which much attention has been paid is which benefits females might gain from copulations outside the pair bond. The 'good genes' hypothesis suggests that females obtain indirect benefits (i.e. good genes for at least part of their offspring). To test predictions from this hypothesis we analysed paternity in a study on great tits (Parus major) over 5 years. Each year 27.8-44.2% of broods contained at least one nestling that derived from a male other than its social father. 5.4-8.6% of all nestlings investigated were extra-pair sired. Males that were cuckolded survived with the same probability to the next year's breeding season as males whose broods did not contain extra-pair young. In addition there were no differences in local recruitment rates of offspring whether they were extra-pair sired or not. Our results do not fit the predictions of the 'good genes' hypothesis. Moreover, patterns of extra-pair paternity in successive years were highly inconsistent, suggesting that factors other than the genetic quality of males play an important role in determining if a particular female or male has extra-pair young in its brood.