A potential consequence of host–parasite coevolution in spatially structured populations is parasite local adaptation: local parasites perform better than foreign parasites on their local host populations. It has been suggested that the generally shorter generation times of parasites compared with their hosts contributes to parasites, rather than hosts, being locally adapted. We tested the hypothesis that relative generation times of hosts and parasites affect local adaptation of hosts and parasites, using the bacterium Pseudomonas fluorescens and a lytic phage as host and parasite, respectively. Generation times were not directly manipulated, but instead one of the coevolving partners was regularly removed and replaced with a population from an earlier time point. Thus, one partner underwent more generations than the other. Manipulations were carried out at both early and later periods of coevolutionary interactions. At early stages of coevolution, host and parasites that underwent relatively more generations displayed higher levels of resistance and infectivity, respectively. However, the relative number of generations that bacteria and phages underwent did not change the level of local adaptation relative to control populations. This is likely because generalist hosts and parasites are favoured during early stages of coevolution, preventing local adaptation. By contrast, at later stages manipulations had no effect on either average levels of resistance or infectivity, or alter the level of local adaptation relative to the controls, possibly because traits other than resistance and infectivity were under strong selection. Taken together, these data suggest that the relative generation times of hosts and parasites may not be an important determinant of local adaptation in this system.