House fly (Musca domestica L) and stable fly (Stomoxys calcitrans [L]) are cosmopolitan pests of humans and livestock. Biogeographical evidence indicates both species were introduced into the New World from somewhere in the Palearctic, Afrotropical and Oriental regions. As introduced species, these two flies are candidates for classical biological control. The present paper will summarize published and unpublished surveys of the parasitoid faunas associated with the two flies in the Old World, and evaluate the hypothesis that elements of those faunas might be sufficiently different from North American counterparts to justify importation and release into the New World.