Effects of the ground motion record orientation on the estimated pseudo-spectral acceleration (PSA) have been investigated and reported in the literature; the statistics of the PSA along the major and minor principal axes differ from that for a random orientation. This is true for California as well as for Mexican records. However, a statistical assessment of the effect of record orientation on the displacement ductility demand is lacking. Such an assessment could be important for gaining confidence in and understanding of using the ductility demand rules for seismic hazard and risk evaluations. The statistical analyses of the effect of orientation on the estimated displacement ductility demand for elastic-perfectly-plastic and bilinear hysteretic (single degree of freedom) systems is carried out in the present study using sets of records from Mexican inslab and interplate earthquakes, and California earthquakes. Based on the obtained statistics, it is suggested that the consideration that the ductility demand is independent of the orientation of the records can be adequate, especially for Tn greater than 0.3 s and elastic-perfectly-plastic hysteretic single degree of freedom systems.