This study develops a war-of-attrition model with the asymmetric feature that one player can be defeated by the other but not vice versa; that is, only one player has an exogenous probability of being forced to capitulate. With complete information, the equilibria are almost identical to the canonical war-of-attrition model. On the other hand, with incomplete information on a player's robustness, a war where both players fight for some duration emerges. Moreover, a player who is never defeated may capitulate in equilibrium, and this player will give in earlier if the other player's fighting costs are greater.