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Measuring terahertz waveforms in terahertz spectroscopy often relies on electro-optic sampling employing a ZnTe crystal. Although the nonlinearities in such zincblende semiconductors induced by intense terahertz pulses have been studied at optical frequencies, a quantitative study of nonlinearities in the terahertz regime has not been reported. In this work, we investigate the nonlinear response of ZnTe in the terahertz frequency region utilizing time-resolved terahertz-pump terahertz-probe spectroscopy. We find that the interaction of two co-propagating terahertz pulses in ZnTe leads to a nonlinear polarization change which modifies the electro-optic response of the medium at terahertz frequencies. We present a model for this polarization that showcases the second-order nonlinear behavior. We also determine the magnitude of the third-order susceptibility in ZnTe at terahertz frequencies,χ⁽³⁾(ω_THz). These results clarify the interactions in ZnTe at terahertz frequencies, with implications for measurements of intense terahertz fields using electro-optic sampling.