Let $\lambda_{q}$ be the irreducible representation of $SL(2,{\mathbb R})$ in $SL(q,{\mathbb R})$. Define a {\em Fuchsian subgroup} of $SL(q,{\mathbb R})$ to be a subgroup conjugate to a discrete subgroup of $\lambda_{q} (SL(2,{\mathbb R}))$. We prove in this paper that the fundamental group of a compact surface does not act properly on the affine space by affine tranformations if its linear part is Fuchsian.