We report that the quenching rate constants of the triplet states of fullerenes (C-70 and C-60) by aromatic amines such as N,N-diethylaniline and N-ethylcarbazole are at least four orders of magnitude smaller than those of the singlet states in methylcyclohexane. Such dramatic differences between the singlet and triplet electron transfer rate constants from a single species, in spite of the states' apparently similar energetics, are unprecedented. Several possible mechanisms are discussed. The data can be rationalized by the presence of structural distortion and biradical character in the triplet state.