Four-wave mixing spectroscopy (FWM) including coherent anti-stokes Raman spectroscopy (CARS) and coherent stokes Raman spectroscopy (CSRS) have been studied for pentacene doped in naphthalene crystals at low temperatures (4.5 to 35 K) in order to investigate nonlinear optical behavior of the third-order nonlinear susceptibility, X('(3)). Further, its application to study of cresyl violet perchlorate embedded in polyacrylic acid and in polyvinyl carbazole has been examined;The theoretical basis for line narrowing has been established for fully resonant four wave mixing for a four-level system. A careful line-narrowing study for the pentacene 755 cm('-1) resonance in naph- thalene illustrates that line narrowing is operative. Temperature dependent studies indicate that the excited state population mech- anism for negative detuning involves phonon hotband absorption. Power broadening data are discussed in terms of dynamic Stark shifts resulting from the site inhomogeneous line broadening of vibronic transitions. Novel temperature-dependent CARS data for positive detuning are presented and tentatively interpreted in terms of the interplay between dephasing induced coherent emission and the temperature dependence of the phonon sideband absorption building on the (0',0) band;Cresyl violet perchlorate in polyacrylic acid shows that the CARS intensity of the excited state resonance at 585 cm('-1) depends on the location of the (omega)(,1)-field within the severely inhomogeneously broadened absorption profile of the dye. It is argued that the linear electron-phonon interaction is an important mechanism for the intensity of the excited state resonance. Time-dependent CARS spectra suggest that the hole burning effect is responsible for the changes of the absolute intensities for ground and excited state vibrational resonances. The absence of line narrowing in the CARS and CSRS spectra is reported and discussed. However, cresyl violet perchlorate in polyvinyl carbazole presents different features in the CARS spectra. The corresponding excited state resonance is very weak at low temperatures. A significant interference from nonreso-;nant to contribution to X('(3)) is reported. Some other experimental results are presented and qualitatively discussed; *DOE Report IS-T-1206. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy.