Extra-pair copulation (EPC) occurred in most socially monogamous bird species. The mechanisms leading to the frequent occurrence of extra-pair offspring (EPO, EPY) in socially monogamous couples, as well as the ‘function’ of EPC, are the subjects of strong debates and raise many unanswered questions. We studied the relationship between extra-pair paternity (EPP) and the different characteristics of males and females in the European pied flycatcher in Western Siberia (Russia). The analysis was based on the genotyping of 232 males, 250 females, 1485 nestlings (250 nests). The European pied flycatchers were predominantly socially and genetically monogamous, but about 20% of birds could be involved in EPP. Loss of paternity tended to be more frequent in one-year-old males. EPCs could be multiple: one individual may have up to three extra-pair partners. The EPP rate was independent of the breeding time. The extra-pair mates of an individual were mainly its near neighbours. The EPC status of an individual was unrelated to most of its morpho-physiological traits. The occurrence of EPP was almost twice as high in females nesting in good quality territories. The fitness of within-pair offspring, EPO, paternal half-sibs of EPO and maternal half-sibs of EPO did not differ statistically significantly. Assuming very low heritability of extra-pair mating, we argued that EPCs could be incidental side effects (by-product) of selection. We believe that the evolution and maintenance of extra-pair mating are the episelective processes in the case of the European pied flycatcher.