We consider the recursive equationx(n+ 1)=A(n)⊗x(n), wherex(n +1) andx(n) are ℝk-valued vectors andA(n) is an irreducible random matrix of sizek × k.The matrix-vector multiplication in the (max, +) algebra is defined by (A(n)⊗x(n))= maxj(Aij(n) +xj(n)). This type of equation can be used to represent the evolution of stochastic event graphs which include cyclic Jackson networks, some manufacturing models and models with general blocking (such as Kanban). Let us assume that the sequence {A(n),n∈ ℕ} is i.i.d. or, more generally, stationary and ergodic. The main result of the paper states that the system couples in finite time with a unique stationary regime if and only if there exists a set of matricessuch thatand the matriceshave a unique periodic regime.