The influence of surface Rayleigh waves (SRWs) on the seismic behavior of three archetype nonconforming reinforced concrete (RC) buildings including weak first story with four, six, and eight stories when subjected to earthquake ground motions (EQGMs) recorded during the strong September 19, 2017 Mw7.1 earthquake in Mexico City, is discussed in this paper. For this purpose, ground acceleration time histories corresponding to the retrograde and prograde components of SRWs were extracted from EQGMs collected at the accelerographic stations placed at the transition and soft soil sites. It was found that the SWRs contribute to about 50% of the median maximum IDR demand (IDRmax) triggered by the as-recorded earthquake ground motions at the ground level of the four- and six-story building models, while their contribution is about 30% of IDRmax for the eight-story building model. It should be noted that that SRWs induce median IDRmax demands to the four-story building model larger than about 11% and 49% than those to the six- and eight-story models, respectively, for soft soil sites. Moreover, the prograde component can trigger IDRmax demands in the four-story building model larger than 73% and 45% than those for the six- and eight-story models, respectively, for the transition sites. Particularly, it was shown that SRWs induce median IDRmax demands in excess of 0.35% at the first level of the archetype building models, which is associated to the light cracking damage state of nonductile RC columns, and even in excess of IDRmax of 0.71% associated to the severe cracking damage state when the record-to-record variability is considered in the IDRmax demand (i.e. the 84th percentile of IDRmax). Although the earthquake ground motion component of the surface Rayleigh waves was negligible in the median IDRmax, this study showed that the effect of the directionality of IDRmax is important for the CH84 station, where significant polarity of spectral ordinates was identified in previous studies.