The effect of continuum couplings in the fusion of the halo nucleus 11 Be on 208 Pb around the Coulomb barrier is studied using a three-body model within a coupled discretised continuum channels (CDCC) formalism. We investigate in particular the role of continuum-continuum couplings. These are found to hinder total, complete and incomplete fusion processes. Couplings to the projectile 1p 1/2 bound excited state redistribute the complete and incomplete fusion cross sections, but the total fusion cross section remains nearly constant. Results show that continuum-continuum couplings enhance the irreversibility of breakup and reduce the flux that penetrates the Coulomb barrier. Converged total fusion cross sections agree with the experimental ones for energies around the Coulomb barrier, but underestimate those for energies well above the Coulomb barrier.Introduction: The existence and the role of the breakup process of weakly bound projectiles in complete fusion and scattering mechanisms have been extensively investigated in recent years both theoretically [1-6] and experimentally [7][8][9][10][11][12][13][14][15][16], but there is not yet any definitive conclusion. There are contradictory theoretical works which predict either the suppression [1][2][3][4] or the enhancement [5] of the complete fusion cross section due to the coupling of the relative motion of the nuclei to the breakup channel.Recent coupled channels calculations for 11 Be+ 208 Pb [6] have shown that the coupling of the relative motion to the breakup channel has two effects, depending on the value of the bombarding energy, namely (i) a reduction of the complete fusion cross sections at energies above the Coulomb barrier due to the loss of incident flux, and (ii) an enhancement of the complete fusion cross sections at energies below the Coulomb barrier due to the dynamical renormalisation of the nucleus-nucleus potential. Using the isocentrifugal approximation and an incoming boundary condition inside the barrier, this calculation did not include the effect of the projectile's halo structure on the monopole projectile-target potential. Nor did it include the excitation to partial waves other than p 3/2 in the continuum, or the continuumcontinuum and bound excited states couplings in either reaction partner. Moreover, only a small interval of energy for continuum states (up to 2 MeV) was considered.The couplings between continuum states have been shown to be crucial to understand the breakup of 8 B on a 58 Ni target at low energy E lab = 25.8 MeV [19,20]. Therefore, it could be expected that continuum-continuum couplings significantly affect the role of breakup process in fusion of halo nuclei around the Coulomb barrier. We believe that