AbstractCo‐evolutionary arms races have provided clear evidence for evolutionary change, especially in host–parasite systems. The evolution of host‐specific races in the common cuckoo (Cuculus canorus), however, is also an example where sexual conflict influences the outcome. Cuckoo females benefit from better adaptation to overcome host defences, whereas cuckoo males face a trade‐off between the benefits of better adaptation to a host and the benefits of multiple mating with females from other host‐races. The outcome of this trade‐off might be genetic differentiation or prevention of it by genetic swamping. We use a simulation model to test which outcome is more likely with three sympatric cuckoo host‐races. We assume a cost for cuckoo chicks that express a host adaptation allele not suited to their foster host species and that cuckoo males that switch to another host‐race experience either a fitness benefit or cost. Over most of the parameter space, cuckoo male host‐race fidelity increases significantly with time, and gene flow between host‐races ceases within a few thousand to a hundred thousand generations. Our results hence support the idea that common cuckoo host‐races might be in the incipient stages of speciation.