A master equation approach including weak exciton-phonon coupling is applied to the exciton dynamics of a dendritic molecular aggregate modeled after a phenylacetylene dendrimer, D25, which exhibits an efficient light-harvesting property. The mechanism of exciton migration from the periphery to the core is studied by analyzing relaxation terms among the exciton states originating in weak exciton-phonon coupling. Partial overlaps of exciton distributions between neighboring exciton states are found to be important for realizing the unique migration behavior by stepwise transfer from the periphery to the core via multi-step exciton states. (C) 2002 Elsevier Science B.V. All rights reserved.