  Let $\mathcal{X}$ be a projective algebraic curve and denote by
$\mathcal{X}^{'}$ its strict dual curve. The map $\gamma:\mathcal{X}
\longrightarrow \mathcal{X}^{'}$ is called (strict) Gauss map of $\mathcal{X}$.
In this manuscript, we study the separable degree of the Gauss map of curves
defined over finite fields. In particular, we give a generalization of a known
result on the separable degree of the Gauss map of plane Frobenius nonclassical
curves. We also obtain a characterization of certain plane strange curves.
