The main objective of this paper is to find structural conditions under which a stochastic game between two players with total reward functions has an ϵ-equilibrium. To reach this goal, the results of Markov decision processes are used to find ϵ-optimal strategies for each player and then the correspondence of a better answer as well as a more general version of Kakutani's Fixed Point Theorem to obtain the ϵ-equilibrium mentioned. Moreover, two examples to illustrate the theory developed are presented.