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In this paper, we consider the problem of efficient estimation for the drift parameter θ ∈ R d in the linear model Z t : = θ t + σ 1 B H 1 (t) + σ 2 B H 2 (t) , t ∈ [ 0 , T ]. Where B H 1 and B H 2 are two independent d-dimensional fractional Brownian motions with Hurst indices H1 and H2 such that 1 2 ≤ H 1 < H 2 < 1. The main goal is firstly to define the maximum likelihood estimator (MLE) of the drift θ, and secondly to provide a sufficient condition for the James-Stein type estimators which dominate, under the usual quadratic risk, the usual estimator (MLE). [ABSTRACT FROM AUTHOR]