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Fling-step and forward directivity are the major consequences of near-fault ground motions as they can impose unexpected seismic demands on structures located in the vicinity of the fault. The pernicious effect of forward directivity on the seismic behavior of structures has been studied widely. However, not much research has been conducted to investigate the influence of fling-step that is related to a large co-seismic displacement. Moreover, the inconsistent results reported in the literature create a scientific challenge about the effect of fling-step on the seismic behavior of long-period structures. In this paper, the effect of fling-step is studied by comparing the displacement ductility demand in various single degree of freedom systems with different natural frequencies and strength reduction factors, subjected to long-period ground motions (generated and as-recorded) with and without fling-step. Subsequently, two 11- and 20-story reinforced concrete buildings are considered and the effect of removing the fling-step on their maximum inter-story drifts is studied. The results indicate that the ratio of the fundamental period of the structure to the fling-pulse period plays an important role and the demands imposed on those systems without fling-step may increase or decrease based on the ground motions type and structural characteristics. Also, a similar trend in the displacement ductility demand was observed in this condition.