Two narrow band gap polymers, polyazopyrrole (PAPY) and polyazothiophene (PATH), were theoretically investigated by means of time-dependent density functional theory (TDDFT) with the B3LYP functional. The most stable trans conformation that would be dominant in the infinite length polymer was discerned, and the chain length dependence of excitation energies of oligomers was studied. By extrapolation, the band gaps of the corresponding trans forms of PAPY and PATH were found to be as low as 1.12 and 0.98 eV, respectively. IR spectra of the oligomers were successfully simulated by density functional theory (DFT) with the B3LYP functional. The results are in good agreement with the reported experimental ones.