Stationary anonymous sequential games with undiscounted rewards are a special class of games that combines features from both population games (in nitely many players) with stochastic games.We extend the theory for these games to the cases of total expected reward as well as to the expected average reward. We show that equilibria in the anonymous sequential game correspond to the limits of equilibria of related nite population games as the number of players grows to in nity. We provide examples to illustrate our results.