A formulation within the London approximation of magnetic ring currents is applied to C60, C70, and their hexa-anions. Contrary to previous approaches, this formulation does not require the identification of closed loops and can therefore be applied to these molecules despite their topological complexity. Knowledge of the ring currents provides a better understanding of their magnetic ring-current susceptibilities. Probe dipoles are used to investigate local spatial variations of the magnetic field induced by the ring currents. In an attempt to evaluate how the carbon chemical shifts are affected by the ring currents, we separate the current into a component circulating above and one below the molecular surface. Assuming a displacement of the negatively charged electronic clouds towards the outside of the molecule, we axe able to understand the relative positions of the carbon NMR lines of C60 and C60(6-).