A theoretical study on the energetics and the structures of lowest triplets of C-60, C-70, C-76, C-78, C-82, and C-84 is reported. Excited state geometries, and excitation and phosphorescence energies, as well as Jahn-Teller distortions for degenerate levels were determined. Zero-field splittings of various triplets were evaluated; the signs and magnitudes of the resulting D and E parameters are quite sensitive to the system and to the symmetry of the particular excited state. Atomic spin density distributions are determined for the lowest triplet states.