  We show a connection between the linear trace Li-Yau-Hamilton inequality for
the Kaehler-Ricci flow and the monotonicity formula for the positive currents.
As an application of the linear trace Li-Yau-Hamilton stated in this paper and
the one proved by Chow-Hamiltonm, we give another proof on the classification
of the limit solutions of the Kaehler-Ricci (Ricci) flow.
