  A Hamiltonian action of a complex torus on a symplectic complex manifold is
said to be {\it multiplicity free} if a general orbit is a lagrangian
submanifold. To any multiplicity free Hamiltonian action of a complex torus
$T\cong (\C^\times)^n$ on a Stein manifold $X$ we assign a certain 5-tuple
consisting of a Stein manifold $Y$, an \'{e}tale map $Y\to \t^*$, a set of
divisors on $Y$ and elements of $H^2(Y,\Z)^{\oplus n}, H^2(Y,\C)$. We show that
$X$ is uniquely determined by this invariants. Furthermore, we describe all
5-tuples arising in this way.
