In　this　paper,　we　study　discrete-time　nonstationary　stochastic　games　with　average　reward　criteria.　The　state　space　is　denumerable　and　the　action　space　of　players　are　Borel　spaces,　while　the　transition　probability　and　reward　functions　can　be　changed　with　time.　Meanwhile,　the　reward　functions　are　allowed　to　be　non-uniformly　bounded.　Under　the　suitable　optimality　conditions,　we　establish　the　average　optimality　equation　and　prove　the　existence　of　Nash　equilibria.　Finally,　we　use　a　queueing　system　to　illustrate　our　results.