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The resonant Raman spectra were obtained for the radical anion of pyromellitic dianhydride in MTHF glass and the radical cation of naphthalene In Freon glass, at $77\circ K$ by using a pulsed tunable dye laser. The laser frequency is tuned to the individual vibrational levels of the absorption band. The resonant Raman thus obtained resembles hot fluorescence in appearance. Overtones and combinations of one specific vibrational mode prevail in the entire spectrum. All of the major Raman active modes are Identified as the totally symmetric modes in the symmetry group of $D2h$. The relative Raman intensity of various modes is calculated by using the dispersion relation of the polarizability theory and the Franck-Condon principle. The overlap integrals are evaluated in the framework of displaced harmonic oscillators. Agreement between experiment and theory is good.