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This paper presents a comprehensive study of residual displacements of the bilinear single degree of freedom (SDOF) systems under the near-fault ground motions (NFGMs). Five sets of NFGMs were constructed in this study, in which the natural ones as well as the synthesized ones were both considered. By way of the nonlinear time history analyses, three different residual displacement spectrums were obtained and analyzed in detail. Utilizing the calculated data, a back propagation (BP) neural network was established to predict the residual displacements of the bilinear SDOF systems under the NFGMs. The results show that the structural parameters, including the strength reduction factor and the post-yield strength ratio, have significant and relatively consistent impacts on the residual displacement spectrum. However, the ground motion characteristics, including the fault type, the closest distance from the site to the fault rupture, the earthquake magnitude, and the site soil condition, exhibit more complex effects on the residual displacement spectrum. In addition, the proposed BP neural network can fully incorporate the parameters affecting the residual displacements of the bilinear SDOF systems under the NFGMs, while having a fairly good accuracy in predicting the residual displacements. [ABSTRACT FROM AUTHOR]