  In this paper we develop two coadjoint orbit constructions for the phase
spaces of the generalised $Sl(2)$ and $Sl(3)$ KdV hierachies. This involves the
construction of two group actions in terms of Yang Baxter operators, and an
Hamiltonian reduction of the coadjoint orbits. The Poisson brackets are
reproduced by the Kirillov construction. From this construction we obtain a
`natural' gauge fixing proceedure for the generalised hierarchies.
