The theory of electronically nonresonant coherent Raman scattering (CRS) with quasi-cw noisy light (I-(2) CRS) is developed for a general material response. The (Raman) resonant-resonant and resonant-nonresonant hyperpolarizability contributions to the 1(2) CRS signal are interferometrically separable. It is found that, in general, the interferometric decay of each of these terms exposes the Raman line shape function in a different manner. Only for a Lorentzian line is their decay identical. Thus, in principle, I-(2) CRS provides a new way to explore the line shape function that is analytically distinct from frequency domain and time domain methods. By way of illustration, the general theory is applied to three common line shapes: Lorentzian (as in the original I-(2) CRS theory), Gaussian, and Voigt. The results are shown to be consistent with the principles of factorized time correlation diagram analysis. (C) 1997 American Institute of Physics.