Why the complete fusion of weakly bound nuclei is enhanced at sub-barrier energies and suppressed above the barrier, P. Gomes, Universidade Federal Fluminense,  Brazil − In the last two decades one has asked whether the complete fusion of weakly bound systems is enhanced or suppressed when compared with the situation where there was no break-up process.  Recent systematic results have shown that the complete fusion cross section is indeed enhanced at sub-barrier energies and suppressed at energies above the barrier, when compared with calculations which do not take into account the coupling to the breakup channel. In this contribution we discuss and explain why such behavior occurs.  We point out the importance of direct transfer and breakup processes and also the recently observed sequential transfer followed by breakup process.  Different behaviors of the dynamic polarization potentials at different energy regions are used to explain the observed fusion excitation functions for several weakly bound systems.