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Compared to the vehicles with conventional steering, the articulated frame steer vehicles (ASV) are known to exhibit lower directional and roll stability limits. Furthermore, the tire interactions with relatively rough terrains could adversely affect the directional and roll stability limits of an ASV due to terrain-induced variations in the vertical and lateral tire forces. It may thus be desirable to assess the dynamic safety of ASVs in terms of their directional control and stability limits while operating on different terrains. The effects of terrain roughness on the directional stability limits of an ASV are investigated through simulations of a comprehensive three-dimensional model of the vehicle with and without a rear axle suspension. The model incorporates a torsio-elastic rear axle suspension, a kineto-dynamic model of the frame steering struts and equivalent random profiles of different undeformable terrains together with coherence between the two tracks profiles.