Coevolutionary models often assume host infection by parasites depends on a single bout of molecular recognition. As detailed immunological studies accumulate, however, it becomes increasingly apparent that the outcome of host-parasite interactions more generally depends on complex multiple step infection processes. For example, in plant and animal innate immunity, recognition steps are followed by downstream effector steps that kill recognized parasites, with the outcome depending on an escalatory molecular arms race. Here, we explore the consequences of such multi-step infection processes for coevolution using a genetically explicit model. Model analyses reveal that polymorphism is much greater at recognition loci than effector loci, that host-genotype by parasite-genotype (Gh x Gp) interactions are larger for the recognition step, and that the recognition step contributes more to local adaptation than the effector step. These results suggest that (1) local adaptation is more likely when fitness measures are related to recognition versus downstream effectors, (2) effector loci, while mechanistically important, are less likely to harbor the Gh x Gp variation that fuels coevolution, and (3) recognition loci are better candidates for genomic hotspots of coevolution.