In　this　paper,　we　consider　the　continuous-time　nonzero-sum　stochastic　games　under　the　constrained　average　criteria.　The　state　space　is　denumerable　and　the　action　space　of　each　player　is　a　general　Polish　space.　The　transition　rates,　reward　and　cost　functions　are　allowed　to　be　unbounded.　The　main　hypotheses　in　this　paper　include　the　standard　drift　conditions,　continuity-compactness　condition　and　some　ergodicity　assumptions.　By　applying　the　vanishing　discount　method,　we　obtain　the　existence　of　stationary　constrained　average　Nash　equilibria.　©　2017　Elsevier　B.V.