High-resolution differential optical transmission measurements of a thin layer of bulk GaAs show anomalous behavior of the lowest energy exciton at low excitation density and temperature. The spectrum shows induced absorption with a superlinear dependence on excitation density with no detectable change in resonance frequency or linewidth. At a temperature dependent excitation density, the anomaly undergoes a transition to a normal response due to excitation-induced dephasing. The results are fully consistent with the polariton picture generalized to include exciton-exciton interactions. [S0031-9007(97)04803-5] PACS numbers: 71.35.Cc, 42.65.Vh, 71.36. + c, 78.55.Cr The coupling of resonant optical radiation below the band gap of direct gap semiconductors is dominated by excitonic resonances which exhibit features similar to atomic systems. However, unlike isolated atoms where the resonant coherent nonlinear optical response arises due to simple saturation when the Rabi flopping frequency approaches the spontaneous emission rate, the nonlinear response of excitons has been shown to be more complex. At moderate excitation levels, the response arises due to many-body effects such as phase space filling and Coulomb interactions including exchange and screening (see [1]). At lower excitation levels (typically between 10 15 and 10 16 excitons͞cm 3 in bulk materials), recent work has shown that strong exciton-exciton scattering leading to line broadening, referred to as excitation-induced dephasing (EID), dominates the nonlinear response [2]. In this paper, we show that in high quality thin films of bulk GaAs, the nonlinear optical response becomes anomalous at reduced excitation levels ͑,10 15 excitons͞cm 3 ͒: A temperature dependent transition occurs leading to induced absorption, a reversal of the sign of the nonlinear response, and apparent multiphoton behavior. We show that the entire range of experimental results is accounted for by the exciton-polariton picture which is generalized to include exciton-exciton interactions.Measurements were made on several high-quality molecular-beam-epitaxy grown GaAs layers (surrounded by Al 0.3 Ga 0.7 As layers between 200 and 500 nm) of various thicknesses (0.2, 0.3, and 0.5 mm). The samples were mounted on a sapphire disk and placed in a helium immersion cryostat following removal of the substrate by chemical etching to allow for optical transmission. The lhhh (light-hole -heavy-hole) degeneracy was lifted by strain [3,4] as shown in the absorption spectrum in Fig. 1(a); the redshift is larger for the lh. The nonlinear response was determined using both cw frequency domain and transient nondegenerate differential transmission (DT) where the excitation and probing beams were independently tunable. The angle between the two beams in the laboratory was ϳ5 ± . The frequency domain DT measurements were made using two frequency-stabilized Coherent 699 Styryl 9 dye lasers (with linewidths of 5 neV) and time domain DT using a subpicosecond Ti:sapphire laser system. For the frequency...