  We present the analogue, for an arbitrary complex reductive group G, of the
elliptic integrable systems of Sklyanin. The Sklyanin integrable systems were
originally constructed on symplectic leaves, of a quadratic Poisson structure,
on a loop group of type A. The phase space, of our integrable systems, is a
group-like analogue of the Hitchin system over an elliptic curve E. We consider
the moduli space of pairs (P,f), where P is a principal G-bundle on E, and f is
a meromorphic section of the adjoint group bundle. We show:
  1) The moduli space admits an algebraic Poisson structure. It is related to
the poisson structures on loop groupoids, constructed by Etingof and Varchenko,
using Felder's elliptic solutions of the Classical Dynamical Yang-Baxter
Equation.
  2) The symplectic leaves are finite dimensional. A symplectic leaf is
determined by labeling, finitely many points of E, each by a dominant
co-character of the maximal torus of G.
  3) Each leaf is an algebraically completely integrable system.
