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We consider a stochastic differential equation with additive fractional noisewith Hurst parameter $H>1/2$, and a non-linear drift depending on an unknownparameter. We show the Local Asymptotic Normality property (LAN) of thisparametric model with rate $\sqrt{\tau}$ as $\tau\rightarrow \infty$, when thesolution is observed continuously on the time interval $[0,\tau]$. The proofuses ergodic properties of the equation and a Girsanov-type transform. Weanalyse the particular case of the fractional Ornstein-Uhlenbeck process andshow that the Maximum Likelihood Estimator is asymptotically efficient in thesense of the Minimax Theorem.

LAN property for stochastic differential equations with additive fractional noise and continuous time observation