The demand assessment is one of the crucial tasks for the energy-based seismic design, it depends upon the characteristics of the seismic action and the structural hysteretic properties. The interest on the definition of seismic demand through energetic parameters, such as equivalent number of yielding excursions (nye), has increased due to the recent introduction of energy-based design approaches into second generation Eurocodes drafts. This work deals with the assessment of seismic cyclic demand on multi-storey structures subjected to a very large ground motions (GMs) set composed of 263 near-fault records with pulse motion. The investigated buildings have a number of stories ranging between two and six, with periods varying from 0.3 s to 1.5 s. The hysteretic properties are defined to represent the typical behaviour of steel and reinforced concrete buildings. Seismic demand is depicted in terms of nye, its dependency on dynamic and hysteretic properties of multi-storey structural systems is shown and discussed also through a comparison with SDOF systems.