Individuals of all vertebrate species differ consistently in their reactions to mildly stressful challenges. These typical reactions, described as personalities or coping strategies, have a clear genetic basis, but the structure of their inheritance in natural populations is almost unknown. We carried out a quantitative genetic analysis of two personality traits (exploration and boldness) and the combination of these two traits (early exploratory behaviour). This study was carried out on the lines resulting from a two-directional artificial selection experiment on early exploratory behaviour (EEB) of great tits (Parus major) originating from a wild population. In analyses using the original lines, reciprocal F(1) and reciprocal first backcross generations, additive, dominance, maternal effects ands sex-dependent expression of exploration, boldness and EEB were estimated. Both additive and dominant genetic effects were important determinants of phenotypic variation in exploratory behaviour and boldness. However, no sex-dependent expression was observed in either of these personality traits. These results are discussed with respect to the maintenance of genetic variation in personality traits, and the expected genetic structure of other behavioural and life history traits in general.