Most experimental studies of epistasis in evolution have focused on adaptive changes—but adaptation accounts for only a portion of total evolutionary change. Are the patterns of epistasis during adaptation representative of evolution more broadly? We address this question by examining a pair of protein homologs, of which only one is subject to a well-defined pressure for adaptive change. Specifically, we compare the nucleoproteins from human and swine influenza. Human influenza is under continual selection to evade recognition by acquired immune memory, while swine influenza experiences less such selection due to the fact that pigs are less likely to be infected with influenza repeatedly in a lifetime. Mutations in some types of immune epitopes are therefore much more strongly adaptive to human than swine influenza—here we focus on epitopes targeted by human cytotoxic T lymphocytes. The nucleoproteins of human and swine influenza possess nearly identical numbers of such epitopes. However, mutations in these epitopes are fixed significantly more frequently in human than in swine influenza, presumably because these epitope mutations are adaptive only to human influenza. Experimentally, we find that epistatically constrained mutations are fixed only in the adaptively evolving human influenza lineage, where they occur at sites that are enriched in epitopes. Overall, our results demonstrate that epistatically interacting substitutions are enriched during adaptation, suggesting that the prevalence of epistasis is dependent on the underlying evolutionary forces at play.