Polarized Raman excitation spectra of various Raman lines in naphthalene and anthracene were measured with high resolution in the pre-resonance region of the lowest allowed electronic transitions. The investigated non-totally symmetric modes exhibit a prominent anti-resonance, but show no polarization dispersion, while the investigated symmetric modes show a hidden anti-resonance, i.e. an anti-resonance with no minimum in the excitation profile, but with a deviating wavenumber behaviour, followed by a strong polarization dispersion. The experimental data are interpreted in terms of a vibronic model using up to three electronic states. It is shown that only when both linearly polarized excitation spectra are measured is it possible to distinguish uniquely between the different scattering models.