Measurement of fusion cross sections for the 6,7 Li + 24 Mg reactions by the characteristic γray method has been done at energies from below to well above the respective Coulomb barriers. The fusion cross sections obtained from these γ-ray cross sections for the two systems are found to agree well with the total reaction cross sections at low energies. The decrease of fusion cross sections with increase of energy is consistent with the fact that other channels, in particular breakup open up with increase of bombarding energy. This shows that there is neither inhibition nor enhancement of fusion cross sections for these systems at above or below the barrier. The critical angular momenta (l cr ) deduced from the fusion cross sections are found to have an energy dependence similar to other Liinduced reactions. PACS number(s) : 25.70. Jj; 25.70. Gh Keywords: NUCLEAR REACTIONS 24 Mg( 6 Li,X), Ec.m. = 4.6-23.7 MeV; 24 Mg( 7 Li,X), Ec.m. = 5.2-22.9 MeV; measured σ γ ; deduced partial, total fusion σ, statistical model, optical model calculations and barrier penetration model calculations.