New experimental and theoretical data on the resonance Raman (RR) spectroscopy of the S-1 and S-2 states of pyrazine are presented. Based on recent ab initio CASSCF (complete-active-space-self-consistent-field) and MRCI (multireference configuration interaction) calculations of Woywod et al. [J. Chem. Phys. 100, 1400 (1994)], we construct a vibronic coupling model of the conically intersecting S-1 and S-2 states of pyrazine, which includes the seven most relevant vibrational degrees of freedom of the molecule. Employing a time-dependent approach that treats the intramolecular couplings in a nonperturbative manner, we calculate RR cross sections for this model, taking explicitly into account the nonseparability of all vibrational modes. The combination of high-level ab initio calculations and multimode propagation techniques makes it possible, for the first time, to make first-principles predictions of RR spectra for vibronically coupled electronic states of an aromatic molecule. The theoretical data are compared to experimental gas-phase RR spectra which have been obtained for five different excitation wavelengths. The comparison reveals that the ab initio predictions match the experimental results in almost every detail.