［Purposes］The existence of strong Nash equilibrium in game problems with set-valued payoffs is discussed. ［Methods］By considering nontrasferable and transferable utilities, the notions of strong Nash nontransferable utility equilibria and strong Nash transferable utility equilibria for games with set-valued payoffs are introduced. ［Findings］Under the regular conditions, the existence theorems of strong Nash nontransferable utility equilibria and strong Nash transferable utility c* -equilibria are obtained. ［Conclusions］This work extends the research scope of set-valued payoff games and extends the existence of cooperative solutions to set-valued payoff games, which provides theoretical support for the application of set-valued payoff games.