This scientific work is the study of the structure of light nuclei ⁶He and ⁶Be in the framework of the three-cluster α+2n-model. The calculation methods have been based on the variational solution of the stationary Schrödinger equation for the relative motion of three clusters in 6He and 6Be nuclei, respectively. The realistic Reid potential has been chosen as the nucleon-nucleon interaction potential, and the potential with even-odd wave splitting has been used for the interaction of the alpha-particle and nucleons. Realistic wave functions of the relative motion of the alpha particle and nucleons in these nuclei and low-lying energy levels have been calculated. The static observables of the 0+ ground state of ⁶He and ⁶Be nuclei, in particular, the root-mean-square charge and material radii and binding energies, have been determined. The obtained values of the root-mean-square charge and material radii of the 6He nucleus confirm the hypothesis of the presence of a neutron halo structure of this nucleus.