  Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra
$g$, and $\xi \colon P \to \Sigma$ a principal $G$-bundle. In earlier work we
have shown that the moduli space $N(\xi)$ of central Yang- Mills connections,
for appropriate additional data, is stratified by smooth symplectic manifolds
and that the holonomy yields a diffeomorphism from $N(\xi)$ onto a certain
representation space $\roman{Rep}_{\xi}(\Gamma,G)$, with reference to suitable
smooth structures $C^{\infty}(N(\xi))$ and
$C^{\infty}(\roman{Rep}_{\xi}(\Gamma,G))$ where $\Gamma$ denotes the universal
central extension of the fundamental group of $\Sigma$. Given an invariant
symmetric bilinear form on $g^*$, we construct here Poisson structures on
$C^{\infty}(N(\xi))$ and $C^{\infty}(\roman{Rep}_{\xi}(\Gamma,G))$ in such a
way that the mentioned diffeomorphism identifies them. When the form on $g^*$
is non-degenerate the Poisson structures are compatible with the
stratifications where $\roman{Rep}_{\xi}(\Gamma,G)$ is endowed with the
corresponding stratification and, furthermore, yield structures of a {\it
stratified symplectic space\/}, preserved by the induced action of the mapping
class group of $\Sigma$.
