We report room‐temperature measurements of the nonlinear absorption cross section, &sgr;eh, and the nonlinear refraction coefficient,neh, associated with saturation of excitonic absorption and bandfilling, for high‐quality multiple quantum well (MQW) structures in which each well consists of a highly strained, all binary (InAs)2(GaAs)5short‐period superlattice. The three samples studied, which have effective well thicknesses of 10.7, 14.8, and 18.8 nm, respectively, each display clearly resolved excitonic resonances at room temperature. Picosecond nonlinear transmission and transient grating measurements were performed on each sample in the spectral vicinity of then= 1 heavy‐hole excitonic resonance. The peak values ofnehand &sgr;ehextracted from these measurements are comparable to those measured in high‐quality GaAs/AlGaAs and unstrained InGaAs/InP MQWs. We determine the dependence of &sgr;ehandnehon the width of the quantum wells, and we discuss the fluence dependence of the nonlinearities. Consistency between the differential transmission and transient grating diffraction efficiency is demonstrated via a Kramers–Kronig analysis of the differential transmission spectra.