  Let $\Phi $ be a Drinfeld $\mathbf{F}\_{q}[T]$-module of rank 2, over a
finite field $L=\mathbf{F}\_{q^{n}}$. We will study the cyclic property of the
structure $L^{\Phi}.$ We will prove that the latter is cyclic only for trivial
extensions of $\mathbf{F}\_{q}$.
