The genetic basis of infection in host-parasite interactions has traditionally been considered within the framework of either gene-for-gene (GFG) or matching-allele models. We present an alternative model, termed inverse-gene-for-gene (IGFG), where pathogen infectiousness is determined by parasite recognition of host signals and/or receptors or where there is active host searching by parasites. We show that coevolutionary dynamics under IGFG are both qualitatively and quantitatively different from those of the GFG model, and we suggest that this new approach may be applicable to a range of important host-parasite systems that are not currently catered for by the existing frameworks.