Abstract A strong mainshock is able to trigger several aftershocks during a short time interval, causing additional damage to structures. The effect of the polarity of aftershock ground motions (positive and negative) is of great significance, particularly on the residual displacement (RD) demand. The positive and negative polarity occurs when the direction of aftershock is the same and the opposite of that of mainshock, respectively, while these are only two of the various situations of the incident angle of aftershock with respect to that of mainshock. This study evaluates the sufficiency of the positive and negative polarity in multiple earthquakes for the determination of critical residual displacements of structures by considering various relative differences between the incident angles of sequential earthquakes. The structures are schematized as bi-linear single-degree-of-freedom systems to develop constant-strength spectra in terms of the Normalized Residual Displacement (NRDθ). The results reveal that considering only the conventional aftershock polarity (positive and negative) may not necessarily lead to critical residual displacement demands, and also accounting for the variability of various incident angles for consecutive ground motions is necessary for the reliable evaluation of structures.