International audienceLet {Xn}n≥0 be a V-geometrically ergodic Markov chain with V≥1 some fixed unbounded real-valued function and consider Mn(α)=n−1∑k=1nF(α,Xk−1,Xk), \alpha\in\mathcalA\in \mathbbR for some real-valued functional F(⋅,⋅,⋅). Define the M−estimator αn such that M_n(\widehat \alpha_n) \leq \min_{\alpha\in\mathcalA} M_n(\alpha) + c_n with cn, n≥1 some sequence of real numbers decreasing to zero. Under some standard regularity assumptions, close to that of the i.i.d case, and under the moment assumption (∂α∂F(α,x,y)+∂α2∂2F(α,x,y))3+ε≤C(V(x)+V(y)) for some constants ε>0 and C>0, the estimator αn satisfies a Berry-Esseen theorem uniformly with respect to the underlying probability distribution of the Markov chain