The majority of species interact with at least several others. We develop simple genetic models of coevolution between three species where interactions are mediated by quantitative traits. We assume that one of the species has two quantitative traits, each of which governs its interaction with one of the other two species. We use this model to explore how genetic correlations between the two traits in the multivariate species shape the evolutionary dynamics and outcomes of three species interactions. Our results suggest that genetic correlations are most important when at least one of the interactions is between a predator and prey or parasite and host. In these cases, genetic correlations between traits lead to a wide variety of novel coevolutionary outcomes and dynamics. In particular, genetic correlations can affect the existence and stability of coevolutionary equilibrium points, and they can lead to recurrent or permanent maladaptation. When the three species interact only as competitors or mutualists, however, genetic correlations have no effect on the outcome of coevolution. In all cases, our results reveal the surprising conclusion that both positive and negative genetic correlations between traits have qualitatively identical effects on coevolutionary dynamics.