The magnitudes of excitonic nonlinearities were compared at 12 K in InGaAs/GaAs multiple quantum well structures with growth directions oriented along the  and  crystal axes by measuring both the steady-state and time-resolved differential transmission spectra. As expected, the spectra for the  sample are indicative of excitonic bleaching at all times and for all excitation levels, and a carrier recombination time of 0.8 ns and a nonlinear cross section (change in absorption coefficient per carrier pair) of ~8×10-14 cm2 are extracted for the  sample. By comparison, for low excitation levels, the spectra for the  sample are consistent with a blueshift of the exciton, indicating a screening of the strain-induced piezoelectric field. At higher excitation levels, the spectra are dominated by excitonic bleaching. Under identical 1 ps pulsed excitation conditions, the magnitudes of the changes in the absorption coefficient caused by screening in the  sample are comparable to those measured for bleaching in the  sample. By contrast, the steady-state changes in the absorption coefficient caused by screening in the  sample are an order of magnitude larger than the changes caused by bleaching in the  sample. It was demonstrated that the larger steady-state response for the  sample is caused by carrier accumulation over the longer (density-dependent) lifetime for that sample and that it is not the result of a larger nonlinear cross section. The slow, nonexponential, density-dependent recombination rates measured for the  sample are consistent with carrier escape and drift to screen the entire multiple quantum well structure and are not consistent with screening within the individual quantum wells.