Single-storey systems with different hysteretic characteristic are subjected to impulse-type short duration and long duration earthquake records to investigate the effects of hysteretic behaviour and ground motion characteristics on the seismic response. EPP, bilinear, Takeda, SINA, and flag-shaped hysteretic models loops are considered and an energy approach is taken to explain the inelastic behaviour. The first part of the work is based on analyses of the single-storey systems without any torsion, however; torsional irregularity is considered in the later analyses. It is shown that structures with the same backbone curve, but different hysteretic characteristics, tend to experience the same maximum response under short duration earthquake records, where there is one major displacement excursion. The likelihood of further displacement in the reverse (i.e. negative) direction is characterized using energy methods and free vibration analyses along with a new proposed “oscillation resistance ratio (ORR)” are employed to improve the understanding of the seismic response. Hysteretic models with low ORR, such as SINA and flag-shaped, are shown to have a greater likelihood of higher absolute displacement response in the negative direction compared with those with fatter hysteretic loops. The understanding of the response in terms of energy reconciles some differences in the ability of initial stiffness versus secant stiffness based methods to predict peak displacement demands with account for different ground motion characteristics. The same peak displacements in the primary direction was also observed for structures with stiffness/strength eccentricities under an impulse-type earthquake record. However, during unloading, the elastic energy stored in the out-of-plane elements is released causing greater displacement on the weak side in the reverse direction.