Among the many Batesian mimetic hoverflies (Diptera: Syrphidae) some have a very precise resemblance to the presumed model (‘good’ or ‘specific’ mimics) while others have a much less precise resemblance (‘poor’ or ‘general’ mimics). Intuitively one might expect that the specific mimics would be commoner and more successful than the general mimics. However, many specific mimics (e.g. Serkomyia silentis, Volucella bombylans) are quite rare, while general mimics are common (e.g. Syrphus ribesii, Episyrphus balteatus and Eristalis intricarius). Similarly, some ant-mimicking spiders from several different families are very good morphological and behavioural mimics of just one species of ant while others have a less detailed resemblance to ants in general. Six hypotheses are presented to explain the occurrence of so many poor mimics, and a theoretical model is outlined (the multi-model hypothesis) which shows how a poor general mimic can have a larger population than a good, specific mimic. This hypothesis may apply to some species of hoverfly and to some ant-mimicking spiders.