The seismic response of mainshock-damaged buildings under aftershocks is an important topic in terms of the lateral response of damaged structures. The majority of current seismic design standards just consider a single earthquake (mainshock/design earthquake) and they don’t take into account the influence of aftershocks on the seismic design process. The aftershocks could have significant effects on the seismic response of mainshock-damaged structures. This situation was reported in some of the previous earthquake events in which the aftershocks caused additional damage to the structures. In this study, the fragility curves for structural and non-structural Drift-Sensitive Components (DSCs) and Acceleration-Sensitive Components (ASCs) of two low-rise mainshock-damaged moment resisting steel and reinforcement concrete buildings under the effect of aftershocks with different intensities were presented. The intensity of the mainshocks was adjusted until the intact buildings experienced three levels of damage states including slight, moderate and extensive damage states. After that, the fragility curve of the structural and non-structural components of the mainshock-damaged buildings under the effect of aftershocks was evaluated by the Incremental Dynamic Analysis (IDA). The results show that the effect of aftershocks on the probability of damage to structural and non-structural components of mainshock-damaged structures is related to the level of the initial damage. For slightly and moderately mainshock-damaged buildings, the probability of exceedance of the damage under aftershocks is relatively similar to the intact buildings, however, the aftershocks significantly increase the probability of damage to the extensively mainshock-damaged buildings. Although extensive initial damage causes a significant increase in the probability of damage to non-structural DSCs, the damage probability of non-structural ASCs remains relatively as similar to intact buildings. Regarding the HAZUS manual, the results show that the probability of damage exceedance of the structural components is higher than non-structural ASCs, however, the opposite observation was reported from the previous earthquakes. Therefore, in this study, four levels of damage threshold for non-structural ASCs are proposed.