We investigate the nonlinear response of terahertz (THz) metamaterial perfect absorbers consisting of electric split ring resonators on GaAs integrated with a polyimide spacer and gold ground plane. These perfect absorbers on bulk semi-insulating GaAs are characterized using high-field THz time-domain spectroscopy. The resonance frequency redshifts 20 GHz and the absorbance is reduced by 30% as the incident peak field is increased from 30 to 300 kV/cm. The nonlinear response arises from THz field driven interband transitions and intervalley scattering in the GaAs. To eliminate the Fresnel losses from the GaAs substrate, we design and fabricate a flexible metamaterialsaturable perfect absorber. The ability to create nonlinear absorbers enables appealing applications such as optical limiting and self-focusing.authors would like to thank the Boston University Photonics Center for technical support.