Using the zero-field quantum-beat technique after beam-foil excitation the authors determine fine-structure and hyperfine-structure parameters of doubly excited Li I 1s2P 2 4P at 60.8 eV above the ground state from the multiplet at 3714 AA. The data interpretation uses simultaneously experimental results from both stable Li isotopes, 6Li and 7Li. The values for the fine-structure splittings are E52/-E32/=(-57+or-8) GHz E52/-E12/=(1.36+or-0.07) GHz. The one-electron parameters of the hyperfine structure are as(6Li)=5.58+or-0.09) GHz a0(6Li)=(0.023+or-0.015) GHz.