Abstract Simultaneous fits have been made to 44 6Li data sets covering the mass range 24–208 and the energy range 13–156 MeV in order to determine an average (“global”) optical-model potential for 6Li scattering. A similar study has been made for 25 7Li data sets over the same mass range and an energy range of 28–88 MeV to find an average 7Li potential. With Saxon-Woods form factors, constant values may be used for all parameters except for the depth of the imaginary potential which decreases in magnitude with increasing mass. The necessity of energy dependence. Coulomb correction and (for 7Li) a symmetry term is investigated. The variation of the integral properties of the potentials is discussed, and also a comparison is made for the two projectiles. Application of the global potentials is made to inelastic scattering and single-nucleon transfer reactions.