  In this paper, we construct a set of new functionals of Ricci curvature on
any Kaehler manifolds which are invariant under holomorphic transfermations in
Kaehler Einstein manifolds and essentially decreasing under the Kaehler Ricci
flow. Moreover, if the initial metric has non-negative bisectional curvature,
using Tian's inequality, we can prove that each of the functionals has uniform
lower bound along the flow which gives a set of integral estimates on
curvature. Using this set of integral estimates, we are able to show the
following theorem: Let M be a Kaehler-Einstein surface with positive scalar
curvature. If the initial metric has nonnegative sectional curvature and
positive somewhere, then the Kaehler-Ricci flow converges exponentially fast to
a Kaehler-Einstein metric with constant bisectional curvature.
