A model is constructed for the local aromaticity of fullerenes and nanotubes. Starting from three infinite series of cylindrical fullerenes, each based on expansion of C-60 along one of its distinct rotational axes, systematics in global and local aromaticity are derived with simple graph-theoretical methods. Confirmed by ab initio calculations on typical members of each series, these results lead to a general model in which, starting from the positions of the (paratropic) pentagonal rings in the structure, the general pattern of local aromaticity can be constructed, enabling the classification of hexagons by their relative aromaticity. Calculated nucleus-independent chemical shifts (NICS) for fullerene isomers can be rationalized in the new model, In particular, in this pentagon-proximity model, every leapfrog fullerene C-3n is predicted to have a complete covering by (n/2 + 2) disjoint paratropic rings: the 12 pentagons and those (n/2 - 10) hexagons derived from the parent C-n structure, leaving a connected network of diatropic hexagons everywhere else.