We present a class of evolutionary games involving large populations that have many pairwise interactions between randomly selected players. The fitness of a player depends not only on the actions chosen in the interaction but also on the individual state of the players. Players stay permanently in the system and participate infinitely often in local interactions with other randomly selected players. The actions taken by a player determine not only the immediate fitness but also the transition probabilities to its next individual state. We define and characterize the Evolutionary Stable Strategies (ESS) for these games and propose a method to compute them.