The behaviour of long–distance migratory birds is assumed to partly be under the influence of genes, as demonstrated by selection experiments. Furthermore, competition for early arrival among males may lead to condition–dependent migration associated with fitness benefits of early arrival achieved by individuals in prime condition. Here I present field data on the repeatability and the heritability of arrival date in a trans–equatorial migratory bird, the barn swallow Hirundo rustica, and I test for a genetic correlation between arrival date and the expression of a condition–dependent secondary sexual character.The repeatability was statistically significant and the heritability of arrival date was estimated to be 0.54 (s.e. = 0.15). There was no significant evidence of this estimate being inflated by environmental or maternal condition during rearing. Arrival date and migration are condition dependent in the barn swallow, with males with the most exaggerated secondary sexual characters also arriving the earliest. There was a significant genetic correlation between arrival date and tail length in male barn swallows, providing indirect evidence for a genetic basis of this condition dependence. Given the high level of heritability, arrival date could readily respond to selection caused by environmental change.