Molecular dynamics simulations have been carried out to explore the structural properties of Li and Li+ confined inside single-walled carbon nanotubes (SWCNTs) and fullerene molecules. C-Li, C-Li+, Li-Li and Li+-Li+ interactions have been represented by pair functions and parameterized for the corresponding interactions. C-C interactions have been modeled by Tersoff potential. Open-ended SWCNTs with various sizes and chirality, as well as fullerenes with various sizes have been considered in the simulations. C-Li interaction is stronger than that of C-Li+. Endohedral Li+ doping caused structural deformations in C60. It has been found that for both Li and Li+ cases endohedral doping is favorable with respect to exohedral doping. This result is valid for both fullerenes and nanotubes.