The investigation of the reaction dynamics induced by light weakly-bound nuclei at Coulomb barrier energies received a quite significant boost with the advent of Radioactive Ion Beams (RIBs). These studies were originally motivated by the fact that calculations predicted either the enhancement or the hindrance of the sub-barrier fusion cross section. However, it was soon realized that breakup related effects largely increased the sub-barrier total reaction cross section and that this enhancement was mainly due to direct processes. Within this framework, we investigated the reaction dynamics induced at near-barrier energies by 8B (Sp = 0.1375 MeV) and 7Be (S_alpha = 1.586 MeV) on a 208Pb target. The experiment with the 8B RIB was performed with the CRIB facility, whereas the system 7Be+208Pb was studied at LNL (Italy). The elastic scattering differential cross sections, the angular distributions for the main reaction products as well as the theoretical analysis will be presented.