A growing number of studies support a tendency toward preferential host switching, by parasites and pathogens, over relatively short phylogenetic distances. This suggests that a host switch is more probable if a potential host is closely related to the original host than if it is a more distant relative. However, despite its importance for the health of humans, livestock, and wildlife, the detailed dynamics of preferential host switching have, so far, been little studied. We present an empirical test of two theoretical models of preferential host switching, using observed phylogenetic distributions of host species for RNA viruses of three mammal orders (primates, carnivores, and ungulates). The analysis focuses on multihost RNA virus species, because their presence on multiple hosts and their estimated ages of origin indicate recent host switching. Approximate Bayesian computation was used to compare observed phylogenetic distances between hosts with those simulated under the theoretical models. The results support a decreasing sigmoidal model of preferential host switching, with a strong effect from increasing phylogenetic distance, on all three studied host phylogenies. This suggests that the dynamics of host switching are fundamentally similar for RNA viruses of different mammal orders and, potentially, a wider range of coevolutionary systems.