Local adaptation of parasites to their sympatric hosts has been investigated on different biological systems through reciprocal transplant experiments. Most of these studies revealed a local adaptation of the parasite. In several cases, however, parasites were found to be locally maladapted or neither adapted nor maladapted. In the present paper, we try to determine the causes of such variability in these results. We analyse a host–parasite metapopulation model and study the effect of several factors on the emergence of local adaptation: population sizes, mutation rates and migration rates for both the host and the parasite, and parasite generation time. We show that all these factors may act on local adaptation through their effects on the evolutionary potential of each species. In particular, we find that higher numbers of mutants or migrants do, in general, promote local adaptation. Interestingly, shorter parasite generation time does not always favour parasite local adaptation. When genetic variability is limiting, shorter generation time, via an increase of the strength of selection, decreases the capacity of the parasite to adapt to an evolving host.