In this work J(13C,13C) coupling constants and the principal components of nuclear magnetic shielding constants in the C60, C70, and C60( 6 - ) fullerenes are calculated at the B3LYP/cc-pCVDZ-sd level using optimized B3LYP/cc-pCVDZ geometries. Indirect spin-spin couplings are utilized to study local diamagnetic ring currents in fullerenes. In unsaturated carbon containing compounds, the Fermi contact (FC) contribution to long-range nJ(13C,13C) (n>4) coupling constants is mainly transmitted through the mobile π-electronic system following a few simple rules: the alternating sign-rule and the pathway invariance. Besides, the absolute value of such a coupling decreases slowly when increasing the number of bonds separating the coupled nuclei. Without explicitly addressing the controversial topic of the aromaticity of fullerenes, we show that the π-transmitted components of the FC contribution provide information on factors affecting ring currents in fullerenes.