This paper analyses the principles of stable cooperation for stochastic games. Starting from the non-cooperative version of a discounted, non zero-sum stochastic game, we build its cooperative form and find the cooperative solution. We then analyse the conditions under which this solution is stable. Principles of stability include subgame consistency, strategic stability and irrational behaviour proof of the cooperative solution. We finally discuss the existence of a stable cooperative solution, and consider a type of stochastic games for which the cooperative solution is found and the principles of stable cooperation are checked.