ABSTRACTCoevolutionary theory predicts that the most common long‐term outcome of the relationships between brood parasites and their hosts should be coevolutionary cycles based on a dynamic change selecting the currently least‐defended host species, given that when well‐defended hosts are abandoned, hosts will be selected to decrease their defences as these are usually assumed to be costly. This is assumed to be the case also in brood parasite‐host systems. Here I examine the frequency of the three potential long‐term outcomes of brood parasite–host coevolution (coevolutionary cycles, lack of rejection, and successful resistance) in 182 host species. The results of simple exploratory comparisons show that coevolutionary cycles are very scarce while the lack of rejection and successful resistance, which are considered evolutionary enigmas, are much more frequent. I discuss these results considering (i) the importance of different host defences at all stages of the breeding cycle, (ii) the role of phenotypic plasticity in long‐term coevolution, and (iii) the evolutionary history of host selection. I suggest that in purely antagonistic coevolutionary interactions, such as those involving brood parasites and their hosts, that although cycles will exist during an intermediate phase of the interactions, the arms race will end with the extinction of the host or with the host acquiring successful resistance. As evolutionary time passes, this resistance will force brood parasites to use previously less suitable host species. Furthermore, I present a model that represents the long‐term trajectories and outcomes of coevolutionary interactions between brood parasites and their hosts with respect to the evolution of egg‐rejection defence. This model suggests that as an increasing number of species acquire successful resistance, other unparasitized host species become more profitable and their parasitism rate and the costs imposed by brood parasitism at the population level will increase, selecting for the evolution of host defences. This means that although acceptance is adaptive when the parasitism rate and the costs of parasitism are very low, this cannot be considered to represent an evolutionary equilibrium, as conventional theory has done to date, because it is not stable.