A quantum-chemical study was performed to investigate the geometrical and electronic structures of a variety of thiophene-based bicyclic polymers [-(C6H2SX)(n)(-)], where X=CH2, SiH2, C=O, C=S, or C=CH2. These two (S and X) types of the bridging groups are different from each other in that S favors the aromatic form of a cyclic polymer and X the quinonoid form. Geometrical structures of the polymers were obtained from AML band calculations and the electronic properties from the modified extended Huckel band calculations. It is predicted that the bicyclic polymers with weak electron-donating groups (CH2 and SiH2 groups) are of the aromatic forms in the ground state and that the polymers with electron-withdrawing groups (C=O, CIS and C=CH2 groups) are of the quinonoid forms as observed in the thiophene copolymers, -[(C4H2S)- (C4H2X)](n)(-). The band gaps (which correspond to the absorption peaks of pi-pi* band transition) of the bicyclic polymers in the ground state are estimated to be in the range of 1.4-1.9 eV. The band gaps were analyzed in terms of the bond-length alternation along the conjugated carbon backbone, the C1-C4 interactions, and the electronic effect of the bridging groups. In comparison with the contributions found in the thiophene copolymers, the contribution from the bond-length alternation to the band gaps decreases, and the contributions from the C1-C4 interactions and the electronic perturbation of S increase. As a result, the band gaps of the bicyclic polymers are about 0.2 eV smaller than those of the corresponding thiophene copolymers.