In this paper the existence of correlated equilibrium payoffs in \(n\)-player stochastic games is studied. A correlation device chooses for every player a private signal before the start of play and sends to each player the signal chosen for him. Then each player can base his choice of an action on the private signal that he has received. Two types of correlation devices are studied (i) stationary devices that choose at every stage a signal according to the same probability distribution independent of the data. (ii) autonomous devices that base their choice of a signal on the previous signal but not on any previous observation. The following results are obtained (a) every stochastic game admits a correlated equilibrium, using an autonomous correlation device. (b) if the game is positive recursive, then the correlation device can be taken to be stationary.