Four new alternating narrow band-gap copolymers containing benzodithiophene, 4,8-dithiophen-2-yl-benzo[1,2-c;4,5-c'-bis[1,2,5]thiadiazole, 4,9-bis(thiophen-2-yl)-6,7-di(2-ethylhexyl)-[1,2,5]thiadiazolo[3,4-g]quinoxaline, 5,8-dibromo-2,3-bis(5-octylthiophen-2-yl)quinoxaline, and 4,7-bis(5-bromothiophen-2-yl)benzo[1,2,5] thiadiazole units are synthesized under Stille reaction conditions. The structures, molecular masses, and physical properties of the copolymers are studied via H-1 NMR spectroscopy, GPC, cyclic voltammetry, and thermomechanical and thermogravimetric analyses. The polymers show solubility and a broad absorption region (with the band gap in the range from 0.81 to 1.53 eV). All of the polymers are photostable in air, and their levels of the highest occupied molecular orbital vary from -4.98 to -5.30 eV. Polymer solar cells based on these copolymers as donors and fullerene PC60BM as an acceptor show open-circuit voltages in the range 0.16-0.61 V, and the efficiencies of the devices are in the range 0.02-0.49%.