Two- and three-pulse time-delayed degenerate and nondegenerate four-wave mixing (photon echo) experiments have been performed on I-2 in the vapor and in hexadecane solution and on azulene in cyclohexane by using "incoherent" light from a broadband dye laser to achieve femtosecond time resolution. Detailed theoretical analyses, including the cases of both parallel and perpendicularly polarized excitation pulses, are presented along with the experimental data. In I-2 vapor, the signals as a function of delay time tau between the two excitation pulses exhibit beats at a frequency characteristic of the spacing between vibrational levels of the B state near the center laser frequency. The rate of decay of the beats and the symmetry of the signals with respect to rare consistent with partial rotational energy randomization during the 10-20 ns waiting time between excitation and probe pulses. This can be considered as a form of spectral diffusion in the gas phase. The solution phase data on both I-2 and azulene are consistent with no significant inhomogeneous component to the solvent-induced electronic spectral breadth on a time scale of several picoseconds or longer, but the theoretical signals from I-2 are shown to be relatively insensitive to the partitioning of the breadth. The general utility of techniques based on incoherent light for examining femtosecond time scale dynamics in solution phase is evaluated.