The molecular mechanics program MM3 and ab initio self-consistent-field (SCF) calculations are used to study the hydrogenated fullerenes C60H36 and C70H36. Researchers have focused their search for the lowest energy structure of C60H36 On two isomers : one with T symmetry and the other with T-h symmetry. We present Hartree-Fock SCF and gradient-corrected density functional theory calculations that predict that the T isomer is lower in energy than the T-h isomer by up to 97.4 kcal/mol. A class of C70H36 isomers, in which the hydrogens are concentrated in the caps of the C-70 structure and in 1, 2, 3 positions on the fullerene’s 12 five-carbon rings, are studied with MM3 optimizations and SCF (STO-3G basis set) energy point calculations at the MM3 geometries. These isomers could be especially low energy structures of C70H36 because the equatorial region of the fullerene cage contains five linked, benzene-like rings that form a highly conjugated, graphite-like region.