The device for damping yawing motions between a highway motor vehicle and its trailer is composed of a curvilinear damping track (4) acted upon by a friction device (17) which may be a pneumatic device attached to the extremity of the shaft (2); the track (4) may be articulated to a fixed portion of the rear of the truck or flexible enough to absorb lurching and pitching motions. The friction device (13) consists of friction slides (21, 22) pressed against the track(4) by an actuator (27) that may be pneumatic. The intensity of the force it generates varies depending upon the cargo in the trailer and/or vehicle speed in order to automatically adapt the yaw-damping effect. This adaptation is achieved by making the actuator (27) subject to suspension pressure and/or vehicle speed. This invention is of interest to manufacturers of trailers and couplings.