AbstractBuildings located on hill slopes are subjected to additional effects under seismic action compared with those on flat ground. This article presents Incremental Dynamic Analyses of coupled building‐slope systems incorporating topographic amplification, nonlinear slope movement and irregular structural configuration of hill‐side buildings. Two different stable slopes, supporting single and multiple adjacent ductile moment resisting reinforced concrete frame buildings with step‐back configuration, prevalent in Indian and Chinese hilly regions, are modelled and analyzed using the finite element software ABAQUS. A suite of 21 ground motions is incrementally scaled and used to compute the seismic response of the coupled system. Fragility curves for different damage states, derived as lognormal probability distributions in terms of three different Intensity Measures (IMs) and damage probabilities of the considered buildings, are derived and compared. The spectrum‐based IMs (e.g., spectral acceleration at fundamental period, and average of the spectral acceleration over a period range) result in lower record‐to‐record variability, compared with the peak ground acceleration as the IM. The results reveal that ignoring the effect of slope significantly underestimates the fragility for all the damage states.