In winter, dabbling ducks gather in large flocks and males compete not only for food resources but also for mates. Setting up a social hierarchy is one way to reduce the costs of conflicts, but the position in the hierarchy has implications for individuals, for instance their susceptibility to conflict and interference, hence to social stress. We investigated relationships between linear social dominance and corticosterone levels, baseline levels and induced-stress response, in captive male mallards Anas platyrhynchos and pintails Anas acuta during the winter period. We hypothesised that corticosterone responses would reflect the costs associated with social stress. From previous work on dominance and corticosterone in wintering birds, we expected that, where the social hierarchy is linear, there would be 1) no relationship between social ranks and baseline corticosterone levels and (2) a significant positive relationship between dominance ranks and responses to acute stress. Our results demonstrated the existence of a linear hierarchy in both species (hV= 0.95 for mallards and hV= 0.97 for pintails), and we found that pintails had on average more corticosterone than mallards. The relationship between dominance and corticosterone responses followed the predictions, with no differences for baseline levels and an attenuated response to induced-stress for subordinates. We discuss these results in the perspective of the cost–benefits of dominance and wintering strategies of waterbirds.