A structure may be subject to several aftershocks after a mainshock. In many seismic design provisions, the effect of the seismic sequences is either not directly considered or has been underestimated. This study examined the seismic behavior of reinforced concrete (RC) moment-resisting structures with concrete shear walls under seismic sequences. Two three-dimensional structures of short and medium height were designed and analyzed under seven real mainshock–aftershock seismic sequences. The models were loaded and designed according to the Iranian seismic code (4th ed.; Standard No. 2800) and ACI-318. The structures were analyzed using the nonlinear explicit finite element method. The maximum displacement, inter-story drift ratio, residual displacement, and ratio of aftershock PGA to mainshock PGA were investigated and assessed. Because of the high lateral stiffness of the shear walls in addition to their completely elastic behavior, the aftershocks did not increase the inter-story drift ratio or relative displacement in the short structure model. The medium height model under the seismic sequences showed a significant growth in the relative displacement (roughly 25% in some cases), inter-story drift ratio, plastic strain, and residual displacement (42.22% growth on average) compared to the structure that was only subjected to the mainshock. Remarkably, in some cases, the aftershock doubled the residual displacement. Unlike the moment-resisting frames under seismic sequences, the models showed no significant growth in the drift ratio with an increase in height. Assessments indicated that the ratio of aftershock PGA to mainshock PGA is a determinative parameter for structural behavior under seismic sequences, such that high values of this ratio (> 0.6) caused significant increases in the residual and relative displacements.