  Let $G$ be a connected reductive affine algebraic group defined over $\mathbb
C$ and $\mathfrak g$ its Lie algebra. We study the monodromy map from the space
of $\mathfrak g$-differential systems on a compact connected Riemann surface
$\Sigma$ of genus $g \,\geq\, 2$ to the character variety of
$G$-representations of the fundamental group of $\Sigma$. If the complex
dimension of $G$ is at least three, we show that the monodromy map is an
immersion at the generic point.
