Automobile trains and tractor-transport units with trailers and technological machines are trailed vehicles and have a number of common structural and functional properties, the main of which is the presence of coupling and support-turning devices, especially in the longitudinal and transverse dynamics of movement and kinematics. At the same time, the trajectory stability of tractor trains is lower than that of single vehicles. One of the ways to solve the problem of increasing the trajectory stability of the ATrP in rectilinear motion by damping the lateral horizontal vibrations of a two-axle trailer can be attributed to the use of stabilizing traction devices that connect the tractor with the front rotary trolley of a two-axle trailer, as well as the front rotary trolley with the trailer body frame. To stabilize the controlled wheels of vehicles, the longitudinal pins (axes of rotation) of the controlled wheels are installed at an angle in the longitudinal plane. To stabilize the front swivel wheel bogie of a two-axle trailer, the longitudinal tilt of the pin may take place at the connection of this bogie to the trailer frame through a turntable (turntable). The article considers the influence of the longitudinal tilt of the pivot pin of the front bogie of a two-axle trailer on the critical speed separating the regions of damped and undamped oscillations of the two-axle sight, as the main indicator of the stability of the rectilinear movement of the tractor-trailer.