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This paper deals with zero-sum nonstationary stochastic games with countable state and action spaces which include both Shapley's stochastic games  and infinite games with imperfect information studied by Orkin in  . It is shown that any nonstationary stochastic game with a bounded below lower semicontinuous payoff defined on the space of all histories has a value function and the minimizer has an optimal strategy. Moreover, two approximation theorems extending the main results of Orkindoi:10.1090/s0002-9939-1984-0759667-1 fatcat:ryvurku5anbf5itrrjlgtxx6yi