The enemy-release hypothesis for biological invasions supposes that invasive species may be more successful in their introduced ranges than in their native ranges owing to the absence of coevolved natural enemies. Recent studies supporting this hypothesis have found that introduced plants and animals are less parasitized in their introduced ranges than in their native ranges. Expanding on this theory, I hypothesize that the role of enemy release may differ among the introduction, establishment and spread phases of an invasion. I present a simple model indicating that parasite release is unlikely to greatly affect the chance of establishment in populations with and without an immune subpopulation. The specific numerical relationship between the number of individuals introduced and the chance of establishment depends on a relationship between virulence, here conceptualized as the chance for the extinction of a lineage, and the fraction of the population infected at introduction. These results support the idea of a 'filter effect' in which different biological processes regulate the different phases of an invasion.