Metapopulation dynamics can strongly affect the ecological and evolutionary processes involved in host–parasite interactions. Here, I analyse a deterministic host–parasite coevolutionary model and derive analytic approximations for the level of local adaptation as a function of (1) host migration rate, (2) parasite migration rate, (3) parasite specificity and (4) parasite virulence. This analysis confirms the results of previous simulation studies: the difference between host and parasite migration rates may explain the level of local adaptation of both species. I also show that both higher specificity and higher virulence generally lead to higher levels of local adaptation of the species which is already ahead in the coevolutionary arms race. The present analysis also provides a simple geometric interpretation for local adaptation which captures the complexity of the temporal dynamics of host–parasite coevolution.