The energy band structures of coronene and ovalene have been calculated in the tight binding approximation using Slater-type orbitals for carbon. The energy band structures of both excess electrons and holes in coronene consist of two sets of energy bands, corresponding to the two degenerate molecular energy levels of the free molecule, which exhibit a high degree of anisotropy with an average width of 0.05 eV. The energy dependence on the wave vector for k parallel to b* has several unusual features. The behaviour can, however, be understood in terms of energy band-energy band interactions. Minimum values of the mobility, calculated such that the uncertainty principle is not violated, are ca. 5 cm²/V s along the b* axis. The energy band structure of ovalene is comparatively simple, again showing a high degree of anisotropy and large bandwidths (0.1 eV). Minimum values of the mobility are of a similar order to those in coronene.