The hybrid model of the microscopic optical potential (OP) is applied to calculate the 11 Li+p , 10,11 Be+p , and 10,11 Be+12 C elastic scattering cross sections at energies E Li+p elastic scattering, the microscopic large-scale shell model (LSSM) density of 11 Li is used, while the density distributions of 10,11 Be nuclei obtained within the quantum Monte Carlo (QMC) model and the generator coordinate method (GCM) are utilized to calculate the microscopic OPs and cross sections of elastic scattering of these nuclei on protons and 12 C. The depths of the real and imaginary parts of OP are fitted to the elastic scattering data, being simultaneously adjusted to reproduce the true energy dependence of the corresponding volume integrals. Also, the cluster models, in which 11 Li consists of 2n -halo and the 9 Li core having its own LSSM form of density and 11 Be consists of a n -halo and the 10 Be core, are adopted. Within the latter, we give predictions for the longitudinal momentum distributions of 9 Li fragments produced in the breakup of 11 Li at 62 MeV/nucleon on a proton target. It is shown that our results for the diffraction and stripping reaction cross sections in 11 Be scattering on 9 Be, 93 Nb, 181 Ta, and 238 U targets at 63 MeV/nucleon are in a good agreement with the available experimental data.