Earthquake ground motions are strongly affected by the upper tens of meters of the Earth’s crust and consequently local site effects need to be included in any ground‐motion prediction. In ground‐motion prediction equations (GMPEs), it is increasingly common to account for possible nonlinear behavior of near‐surface materials (soil). These nonlinear site terms adjust observations made on soft soil sites to the ground motion expected on bedrock and hence allow these abundant soil records to be used within the regression analysis for the derivation of empirical GMPEs. These nonlinear site terms also allow rapid predictions of the expected ground motions on soil rather than requiring a site‐response analysis to be conducted. In this study, we compare the signature on observed peak ground acceleration as a function of a strain proxy of nonlinear soil behavior within four large strong‐motion databases to the predicted signature from four recent GMPEs, three of which explicitly include nonlinear site terms. We find that observed nonlinearity in the databases, interpreted in terms of strain–stress relationships and reduction of shear modulus, is limited, but even this limited effect is underestimated by the nonlinear site terms of the considered GMPEs, which suggests that predictions from these GMPEs could be biased for soft soil sites but also on bedrock. Some of this mismatch could be explained by the use of the average shear‐wave velocity in the top 30 m () to characterize sites as well as errors in these values.