The vibronic coupling between the first excited S1 (21Ag) and the second excited S2 (11Bu) singlet electronic states in spectroscopy of trans-1,3,5-hexatriene molecule is investigated on the basis of a model consisting of two electronic states coupled by two vibrational modes. Employing a perturbation theory that treats the intramolecular couplings in a perturbative manner, the absorption and resonance Raman cross sections and excitation profiles of this molecule are calculated using the time-correlation function formalism. The non-Condon corrections are included in evaluation of cross sections. The multidimensional time-domain integrals that arise in these calculations have been evaluated for the case in which S0 (11Ag)S2 (11Bu) electronic transition takes place between displaced and distorted harmonic potential energy surfaces. The calculated spectra are in good agreement with the experimental ones. Copyright © 2011 John Wiley & Sons, Ltd.