This paper considers a relationship between the modified strong equilibria of a repeated game and the modified \(\beta\)-core of the component game. Here the strong equilibrium concept is modified so that whenever a coalition S deviates from a given strategy n-tuple \(\bar s=(\bar s_ 1,...,\bar s_ n)\), the strategies \(\bar s_{N-S}\) of the complementary coalition N-S should be the best response for the new strategies of the deviating coalition S. The \(\beta\)-core is modified in the same manner. Then, instead of Aumann's theorem that the strong equilibria of a repeated game coincide with the \(\beta\)-core of the component game, it is obtained that the modified strong equilibria are included in the modified \(\beta\)-core of the component game. This is the main result of this papers.