The equilibrium geometries, heats of formation, and harmonic vibrational frequencies of hydrogenated buckminsterfullerene derivatives C60H60-6n. Containing 1-8 benzenoid units were computed using MNDO and AM1 methods. Although the Hessian indices indicate that all such structures are true minima, the T symmetry structure of C60H36 With four benzene rings is calculated to be the best prospect for experimental characterization. The relative stabilities of the various derivatives are principally controlled by angle strain at the sp2 and sp3 carbon atoms.