Abstract : We consider the Fredrickson and Andersen one spin facilitated model (FA1f) on an infinite connected graph with polynomial growth. Each site with rate one refreshes its occupation variable to a filled or to an empty state with probability p ∈ [0, 1] or q = 1 − p respectively, provided that at least one of its nearest neighbours is empty. We study the non-equilibrium dynamics started from an initial distribution ν different from the stationary product p-Bernoulli measure µ. We assume that, under ν, the distance between two nearest empty sites has exponential moments. We then prove convergence to equilibrium when the vacancy density q is above a proper threshold ¯ q < 1. The convergence is exponential or stretched exponential, depending on the growth of the graph. In particular it is exponential on Z d for d = 1 and stretched exponential for d > 1. Our result can be generalized to other non cooperative models.