We study the ergodic properties of finite-dimensional systems of SDEs driven by nondegenerate additive fractional Brownian motion with arbitrary Hurst parameter H∈2 (0,1).A general framework is constructed to make precise the notions of “invariant measure” and “stationary state” for such a system.We then prove under rather weak dissipativity conditions that such an SDE possesses a unique stationary solution and that the convergence rate of an arbitrary solution towards the stationary one is (at least) algebraic. A lower bound on the exponent is also given.