The present paper deals with the simplified methods currently available for evaluating the seismic demand on structures by means of nonlinear static procedures. In particular, after a brief discussion about the key conceptual assumptions considered by those methods, two alternative procedures for evaluating the demanded ductility induced by seismic actions are outlined. They are the Capacity Spectrum Method (Freeman, 1975; ATC40, 1996) and the so-called N2-Method (Fajfar, 1999; Eurocode 8, 2004). The key dimensionless parameters controlling the predictions of those methods are pointed out considering an elastic-perfectly plastic behaviour and possibly taking into account the effect of linear strain-hardening in the structural behaviour. The two mentioned methods lead to rather different results for the same values of the key parameters describing the non-linear response of structures under seismic shakings. The most significant difference among those models on the demanded ductility deals with the way in which they simulate the possible influence of the actual properties of the cyclic response of structures. In fact, the N2-Method completely neglects such an influence, having been calibrated on particular types of hysteretic behaviours of structures under cyclic actions. On the contrary, the Capacity Spectrum Method takes into account the actual dissipative capacity of structures and the supposed shape of the hysteretic loops characterizing their cyclic response. In particular, it introduces different relationships for defining the equivalent viscous damping corresponding to the demanded ductility. A wide parametric analysis is carried out in this paper with the aim of shedding new light about the actual relevance of the shape of hysteretic loops representing the post-elastic behaviour of structures and their effect on the ductility demand induced by the expected seismic shaking. Finally, the paper proposes a simplified relationship extending the N2-Method to the case of structures with a variable shape of the post-elastic cyclic behaviour.