The Fourier-transform four-wave mixing (FT 4WM) formalism is introduced, developed, and applied to femtosecond optical-heterodyne detected optical Kerr effect data for pyridine liquid. When applied to transient 4WM data obtained with sufficiently short laser pulses, the FT 4WM method generates directly the third-order, nonlinear-optical frequency response of the medium, χ(3), with no pulse-shape approximations, curve-fitting, or assumed models. The frequency-domain representation of the nonlinear-optical transients provides a powerful interpretive tool for the interrogation of the Raman-active vibrational structure and dynamics of materials, including the role of inhomogeneously-broadened, intermolecular vibrational (lattice-like) modes in shaping the transients observed in femtosecond 4WM experiments. We show that the pulse-width dependence of the measured 4WM transients is conveniently described in terms of the spectral-filter effects of the finite-duration/finite-bandwidth optical pulses on the intrinsic frequency response of the medium. © 1990.