An auto-tractor train is a mechanical system consisting of transport and kinematic links connected by articulated links. The motion of a mechanical system is stable if it has a property that ensures the preservation of the character of a given motion, or tends to it after receiving initial disturbances. A mechanical system (tractor, car, trailer) may or may not have stability of movement. This largely depends on the choice of dynamic parameters when designing a trailer train, as well as when completing tractor trains under operating conditions. One of the solutions to the problem of increasing the stability of the rectilinear movement of the ATP can be attributed to the use of stabilizing devices - stabilizers for suppressing lateral vibrations of trailers, designed to reduce (suppress) lateral vibrations of trailers. Stabilizers can be installed between the kinematic links of a tractor train on traction devices (on the towing device of a tractor), or on the support-turning devices of trailers (between the rotary trolley and the trailer frame), which perceive, in addition to traction, the support load. The purpose of the stabilizing devices is to ensure the creation of a force stabilizing moment that prevents the towed trailer link from deviating from the trajectory of the straight-line movement of the tractor after external lateral force impacts on the trailer or to create a force moment that promotes the return of the link to the position corresponding to the straight-line movement of the tractor. The article discusses the issues of the influence of various types of stabilizing devices on the stabilization of the rectilinear movement of trailer links of a tractor train.