In　this　work　we　consider　periodic　problems　for　two-fluid　compressible　Euler-Maxwell　systems　for　plasmas.　The　initial　data　are　supposed　to　be　in　a　neighborhood　of　non-constant　equilibrium　states.　Mainly　by　an　induction　argument　used　in　Peng　(2015),　we　prove　the　global　stability　in　the　sense　that　smooth　solutions　exist　globally　in　time　and　converge　to　the　equilibrium　states　as　the　time　goes　to　infinity.　Moreover,　we　obtain　the　global　stability　of　solutions　with　exponential　decay　in　time　near　the　equilibrium　states　for　two-fluid　compressible　Euler　Poisson　systems.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.