An extensive analysis of the infrared and Raman spectra of p-benzoquinodimethane (p-BQM) has been performed, based on a reanalysis of the vibrational spectra of p-benzoquinone (p-BQ). Optimizations of structure parameters have been carried out at the Hartree-Fock and the second-order Moller-Plesset perturbation levels. Force constants in the Cartesian-coordinate system obtained from molecular-orbital calculations have been transformed into those in a redundancy-free symmetry-coordinate system and then scaled to obtain good fits between the calculated and observed frequencies. The scale factors have been optimized for the observed frequencies of p-BQ and its isotopic species and then have been transferred to the force constants of p-BQM. Features in the Raman and infrared spectra of these compounds and vibrational modes characteristic of the quinoid structure are discussed. The structure parameters, scaled force constants, and vibrational frequencies of p-BQM indicate that this molecule is more benzenoid-like than p-BQ.