The Red Queen hypothesis for the maintenance of sexual reproduction suggests that harmful parasites and pathogens exert selection pressures on their hosts which make asexual reproduction an unstable long-term strategy. We propose, however, that host obligate asexuality can be favoured in the long term, despite the effects of parasites, under the following conditions. First, the host population structure should approximate a metapopulation. Second, the hosts or the parasites should exhibit relatively high levels of dispersal. Third, parasites must disperse independently of their hosts. In support of this view, we present a computer simulation of host-parasite coevolution in a metapopulation. The simulation demonstrates that a large difference between host and parasite dispersal rates favours an obligately asexual host reproductive strategy over an obligately sexual one. This hypothesis may explain the persistence of anciently asexual taxa, such as the bdelloid rotifers, and the patterns of dispersal seen in obligately asexual groups in general.