Evolutionary stability has been discussed as a fundamental issue in single-criterion games. We extend evolutionarily and neutrally stable strategies to multicriteria games. Keeping in mind the fact that a payoff is given by a vector in multicriteria games, we provide several concepts which are coincident in single-criterion games based on partial vector orders of payoff vectors. We also investigate the hierarchical structure of our proposed evolutionarily and neutrally stable strategies. Shapley had introduced concepts such as strong and weak equilibria. We discuss the relationship between these equilibria and our proposed evolutionary stability.