The current seismic regulations neglect the influence of multiple seismic events on the seismic response, which, asalready found in the literature, may strongly affect the seismic structural behavior. Symmetrical and asymmetrical reinforced concrete low-rise frames are investigated here via nonlinear time-history (NLTH) analysis under multiple seismic events, as well as under a respective single seismic event, for comparison purposes. The two horizontal directions, as well as the vertical one, of the ground excitation are considered in the NLTH analysis, assuming the nonlinear behaviour of reinforced concrete sections under strong loading. A simple ratio is defined to express the geometrical in-plan asymmetry of the 3D building frames. The nonlinear response results of the time-history analyses are appropriately plotted by using unitless parameters for an objective evaluation of the seismic behavior of the building frames. The response dimensionless results and plots are presented and discussed in view of the relative geometrical asymmetry of the 3D frames. The effect of the multiple seismic events, along with the effect of a simple geometrical symmetry or asymmetry, is identified and discussed in the presented plots of the seismic structural response. Thus, practical remarks are obtained regarding the role of the geometrical in-plan symmetry or asymmetry of frames for the improvement of the guidelines of the current seismic codes ir order to develop safer structures.