We model the one- and two-photon excitations of polythiophene (PT)in terms of interacting a-electrons and a charge-density-wave (CDW) ground state due to S atoms. The Pariser-Parr-Pople (PPP) model for ir-electrons is modified for a CDW ground state, with all additional Coulomb interactions leading to a site-energy difference of 2 epsilon between the alpha and beta carbons along the PT backbone. The polyene (epsilon = 0) ordering of the one- and two-photon excitations is reversed in nT oligomers with increasing epsilon and standard hydrocarbon parameters, with epsilon = 1.8 eV obtained from 2T and 3T data. The magnitude of epsilon is consistent with atomic charges obtained semiempirically and rationalizes two-photon PT spectra and fluorescence, which indicate S-1 to be one-photon allowed. Polaron and bipolaron excitations of 2T and 3T are obtained exactly within the PPP model at epsilon = 0 and 1.8 eV for the ground-state geometry and compared to experiment. In-gap excitations of anions and cations differ significantly at epsilon = 1.8 eV upon lifting electron-hole symmetry.