Infrared and Raman spectra of perylene and terrylene computed by ab initio methods at the 3-21G level are presented and discussed. The pattern of the Raman spectrum is very similar to that observed experimentally (even if unsealed frequencies are too high) and characterized by few strong totally symmetric bands; moreover, the agreement between calculated and measured Raman intensities is quite good. Vibrational contributions to second-order molecular hyperpolarizability, gamma(ijkl)(r), for the two compounds studied are calculated starting from ab initio Raman frequencies and intensities. The values obtained for the orientation average ([gamma(r)]=2.60X10(-35) for perylene and 1.90X10(-34) esu for terrylene) are in extremely good agreement with the experimental determination. In the case of perylene we have also calculated the electronic second-order hyperpolarizability, gamma(ijkl)(e), with an ab initio finite field method at the same level of approximation (3-21G) as the vibrational analysis. For completeness the case of naphthalene has also been considered. The comparison between gamma(e) and gamma(r) leads to the conclusion that in this class of materials the vibrational contribution to gamma is large and very close to the electronic one. The results obtained are interpreted by means of the effective conjugation coordinate (ECC) theory and a description is made of the a coordinate of these molecules.