The coherent nonlinear optical properties of direct gap semiconductors have been investigated by picosecond time resolved degenerate four-wave mixing (DFWM). The experiments were performed at low temperatures and with low, or moderate, excitation densities, focusing on the strong excitonic resonance enhancement of the nonlinear optical susceptibility x(3). Free exciton transitions, including two-photon absorption to the biexciton state and induced exciton-biexciton transitions, contribute strongly to x(3)in CdSe, whereas the contribution from excitons, localized by fluctuating potentials, dominates in the mixed crystals CdSexS1-x,and in the layered GaSe. The magnitudes of the coherent and the incoherent contributions to the nonlinear signal are compared, and the response time (dephasing time) of the coherent nonlinear signal is investigated in detail. The observed dephasing times are dominated by exciton-exciton collisions in CdSe, by exciton-phonon interaction in CdSexS1-x, and by disorder and phonon induced intervalley scattering in GaSe.