We study a two-player nonzero-sum Dynkin game in continuous time, where the payoff functions are not required to satisfy the standard “war of attrition”-type order condition. To address this generalised setting, we establish a verification theorem that yields a system of variational inequalities characterising both the players’ payoffs and their strategies at certain Nash equilibria. As an application, we examine convertible bond problems with tax benefits. In the first example, we demonstrate the existence of multiple nontrivial Nash equilibria. In the second example, we consider the case where a bondholder possesses two units of convertible bonds and may convert them sequentially. This leads to a two-stage nonzero-sum game that also violates the usual order condition. A Nash equilibrium is identified numerically. Joint work with David Hobson and Edward Wang.