Coevolution between parasites and hosts or predators and prey often involves multiple species with similar kinds of defenses and counter-defenses. Classic examples include the interactions between phytophagous insects and their host plants, thick-shelled invertebrates and their shell-crushing predators, and ungulates and their predators. There are three major hypotheses for the nonequilibrium coevolutionary dynamics of these multispecific trophic interactions: escalation in traits, cycles in traits leading to fluctuating polymorphisms, and coevolutionary alternation. The conditions under which cycles and escalation are likely to occur have been well developed theoretically. In contrast, the conditions favoring coevolutionary alternation—evolutionary fluctuations in predator or prey preference driven by evolutionary shifts in relative levels of prey defense and vice versa—have yet to be identified. Using a set of quantitative coevolutionary models, we demonstrate that coevolutionary alternation can occur across a wide range of biologically plausible conditions. The result is often repeated, and potentially rapid, evolutionary shifts in patterns of specialization within networks of interacting species.