Summary form only given. The nonlinear optics near the fundamental absorption edge is commonly formulated in terms of a limited number of material parameters characterizing the strength of specific nonlinear processes. Once the nonlinear response function underlying these material parameters is known, one can optimize the relevant nonlinear optical effect for specific device applications. This study is focused on optical nonlinearities at quasi-resonant conditions in the picosecond-pulse regime, where excitonic correlations, such as biexcitonic resonances, contribute prominently to the physical processes. Using a microscopic theory, we have calculated systematically the parameter dependencies of some representative figures of merit, nonlinear phase shift Δφ and differential transmissivity AT, which provide complementary information on the nonlinear susceptibility-χ(3):Δφ∼Reχ(3), ΔT∼Imχ(3), approximately. We will show in detail how the various aspects of excitonic dynamics affect these quantities around the exciton resonance.