Abstract: To quantitatively assess the secondary damage caused by aftershocks on a mainshock-damaged structure, this study focuses on the incremental damage spectra of mainshock-aftershock sequence-type ground motions. A set of 533 real mainshock-aftershock sequences were selected as the input. The index proposed by Park and Ang (1985) was used to define structural damage due to earthquake. The incremental damages induced by aftershocks were quantified by the difference between the structural damages caused by mainshocks and mainshock-aftershock sequences. Results show that the incremental structural damages due to aftershocks show a large degree of variability. Some mainshock-aftershock sequences cause significant incremental damages as oppose to others. In comparison to the structures with short natural periods, the ones with medium-to-large natural periods show larger incremental damages under mainshock-aftershock sequences. If the predominant period of the mainshock is greater than that of the corresponding aftershock, this mainshock-aftershock sequence can be viewed as the unfavourable one, which probably causes significant incremental structural damages.