The excess electron and hole band structures of naphthalene, anthracene, and several polyphenyls have been calculated in the tight binding approximation. In addition the anisotropy and the pressure dependence of the mobility tensor has been calculated in the constant-free-time and the constant-free-path approximations. The molecular wavefunctions were represented in the LCAO approximation using Hückel coefficients with the carbon atomic orbitals represented by the best available Hartree-Fock SCF carbon 2p ground-state function involving a linear combination of four Slater-type functions. By this choice of atomic orbitals, we hope to account properly for the behavior of the wavefunction at the large internuclear distances relevant to this problem. All of the above compounds are characterized by a crystal structure containing two molecules per unit cell. There are, therefore, two bands for both the electron and the hole cases. The bandwidths are calculated to be of the order of 0.1 eV. In the a-1 and b-1 directions, the symmetric and antisymmetric bands are degenerate at the zone edge. The electron bands are appreciably split in the c-1 direction. Although there is no attempt to make absolute calculations of the mobility, the experimental data seem to be in adequate agreement with the scattering models considered. Inferences can be drawn which suggest that further understanding of the mobility will arise from a detailed investigation of the interaction of the charge carriers and the intermolecular and intramolecular vibrations.