The endogenous order of moves is analysed in a unionised Cournot duopoly with managerial delegation and firm‐specific unions, where firms choose whether to set quantities sequentially or simultaneously. It is shown that, in contrast to the standard duopoly with profit‐maximising firms where both firms prefer to be the leader and thus simultaneously chosen quantities emerge as an endogenous equilibrium, a rich set of equilibrium outcomes may occur. In particular, the result of sequential choices, which reverses the conventional wisdom in regard to Cournot duopolies, emerges as the endogenous equilibrium when the union's wage orientation is sufficiently high.