  In the present paper, we prove a stability theorem for the Kaehler Ricci flow
near the infimum of the functional E_1 under the assumption that the initial
metric has Ricci > -1 and |Riem| bounded. At present stage, our main theorem
still need a topological assumption (1.2) which we hope to be removed in
subsequent papers. The underlying moral is: if a Kaehler metric is sufficiently
closed to a Kaehler Einstein metric, then the Kaehler Ricci flow converges to
it. The present work should be viewed as a first step in a more ambitious
program of deriving the existence of Kaehler Einstein metrics with an arbitrary
energy level, provided that this energy functional has a uniform lower bound in
this Kaehler class.
