Fling-step and forward-directivity effects of near-fault ground motions can produce long duration intense velocity pulses in the horizontal direction, making unexpected ductility demand in reinforced concrete (r.c.) spatial framed structures designed in accordance with current seismic codes. In practice, simplified percentage-rule methods, in which a coefficient indicates the mutual participation between the two horizontal ground motions, are generally used to deal with the problem of the critical incidence angle of bi-directional ground motions. In order to investigate the orientation of the horizontal components of near-fault earthquakes that yields the maximum inelastic structural response, this work considers six-and twelve-storey r.c. framed buildings with symmetric plan are designed for a high-risk seismic region in line with the provisions of the Italian seismic code. A lumped plasticity model is used to describe the inelastic behaviour of the r.c. frame members, with flat surfaces approximating the axial load-biaxial bending moment domain at the end sections where inelastic deformations are expected. A multicomponent nonlinear incremental dynamic analysis is carried out with reference to different incidence angles of bi-directional earthquakes, which are scaled to four intensity levels to encompass a wide range of structural behaviours. To this end, seven nearfault ground motions are selected, based on the design hypotheses adopted for the test structures.