This talk is devoted to Hamiltonian actions
of reductive groups on affine Poisson varieties. More
precisely, let $X$ be an affine Poisson variety
with a Hamiltonian action of a reductive group
$G$ and the moment map $mu:X
ightarrow Lie(G)$.
We prove that, under some additional restrictions,
the corresponding morphism of quotients
$X//G
ightarrow Lie(G)//G$ is equidimensional. Next,
we study the affine Stein factorization of this
morphism. Our results partially generalize those
of F. Knop.