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The theory of sexual conflict predicts that sexual coevolution will be very dynamic, with in principle perpetual evolutionary arms races and chases. These arms races are expected to stop once the costs of conflict adaptations become too high. We argue that this prediction is contingent on specific assumptions about the sexual interaction and the adaptations involved in the arms race. More generally, evolutionary arms races stop when the fitness benefit of further escalations is outweighed by the fitness costs. For this it is not necessary that the absolute costs of conflict must be high at the stable state, or that the population fitness must be decreased at equilibrium. We expect the outcome of sexual antagonistic coevolution to be determined by the possibility to reach compromises and by the relative ability of each sex to control the outcome of the interaction. We exemplify with a theoretical conflict model, which leads to population extinction when conflict is settled by armaments with expression-level determined costs. The model predicts a compromise with small conflict costs for the population, if costs are in addition determined by the extent of conflict between the sexes, which may be the case when the cost depends on behavioural antagonism.