In this paper we shall present a proof for the existence of limiting average ε-equilibria in non-zero-sum repeated games with absorbing states, i.e., stochastic games in which all states but one are absorbing. We assume that the action spaces shall be finite; hence there are only finitely many absorbing states. A limiting average ε-equilibrium is a pair of strategies (σ ε , τ ε , with ε > 0, such that for all σ and τ we have γ1(σ, τ ε ) ≤ γ1(σ ε , τ ε ) + ε and γ2(σ ε ,τ) ≤ γ2(σ ε τ ε ) + ε. The proof presented in this chapter is based on the publications by vrieze and thuijsman  and by thuijsman . Several examples will illustrate the proof.keywordsstationary strategystochastic gamerepeated gameaverage rewardsmall trianglethese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.