Calculations of the vibronic structure in electronic absorption and fluorescence spectra of a large polyatomic molecule based on time- and frequency-domain approaches beyond the Condon approximation are developed. In time-domain approach, the molecular spectra are expressed in terms of Fourier transforms of appropriate time correlation functions, which are evaluated in closed form for displaced–distorted– rotated harmonic potential surfaces at finite temperature. In frequency-domain approach, use is made of the Franck–Condon factors which were evaluated in closed form for the same potential surfaces in our previous work (J. Molec. Spectrosc. 194 (1999) 179). The vibronic structure in dipole-forbidden (but vibronic-allowed) 11Ag ↔ 21Ag and dipole-allowed 11Ag ↔ 11Bu electronic transitions of alltrans- 1,3,5,7-octatetraene have been calculated and compared with experimental data as illustrations of the approaches. Our vibronic structure calculations support the hypothesis that a sudden opening of a non-radiative decay channel occurs at 21Ag vibronic levels with energies larger than about 2100 cm_1