  We study Hamiltonian dynamics of gradient Kaehler-Ricci solitons that arise
as limits of dilations of singularities of the Ricci flow on compact Kaehler
manifolds. Our main result is that the underlying spaces of such gradient
solitons must be Stein manifolds. Moreover, on all most all energy surfaces of
the potential function f of such a soliton, the Hamiltonian vector field V_f of
f, with respect to the Kaehler form of the gradient soliton metric, admits a
periodic orbit. The latter should be impotant in the study of singularities of
the Ricci flow on compact Kaehler manifolds in light of the ``little loop
lemma'' principle due to the second author.
