We have extended our study of the vibronic absorption spectrum in condensed matter [S. A. Egorov, E. Rabani, and B. J. Berne, J. Chem. Phys. 108, 1407 (1998)] to the case when the electronic dephasing rate is slow compared to the vibrational relaxation rate in both electronic states. We find that under such circumstances, unlike the case of fast electronic dephasing, treating all nuclear degrees of freedom classically provides better agreement with the exact quantum treatment than the mixed quantum-classical approximation. These results are consistent with the conclusions reached by Bader and Berne in their study of mixed quantum-classical treatments of vibrational relaxation processes.