The photoexcited triplet states of fullerenes C-60 and C-70 dissolved in a nematic liquid-crystal solvent have been investigated using time-resolved EPR (TR-EPR) spectroscopy. Triplet spectra composed of two lines with opposite polarization (enhanced absorption and emission) and small line widths have been recorded for C-60, but much broader lines are recorded for C-70. The Jahn-Teller dynamic distortion of C-60 is responsible for the motional narrowing of the triplet lines, and the partial orientation induced by the nernatic solvent removes the degeneracy of the two triplet transitions giving rise to a doublet of lines. Broad features appearing at low temperatures in the nernatic phase are attributed to the local disorder induced by the dissipation of excess energy in the photoexcitation process. The time decay of the TR-EPR signals is explained by a kinetic model for the spin-level populations including spin relaxation and selective decay of the spin sublevels.