FIELD: automobile; tractor trains. SUBSTANCE: coupling stabilizing device of a single-axle trailer comprises a traction lever connected by the front part to the tractor through a hinge mount made in the form of a cross-shaped joint comprising a cross formed from a cross piece and a cross pin fixedly connected to each other by the horizontal axis of the cross. The horizontal axis of the crosspiece is connected to the traction lever by means of a fork, and the crosspiece pin is configured for rotation relative to its axis in the upper and lower eyes of the fork-flange. The lower end of the cross pin is installed in a longitudinal slot made in the lower eye of the fork-flange with the ability to move along this slot and is connected by means of a hinge to the transverse horizontal axis with the rod of the double-acting working hydraulic cylinder. The upper end of the cross pin is connected to the upper eye of the fork-flange by means of a ball joint. A double-acting hydraulic cylinder is installed on the upper part of the fork-flange. EFFECT: stabilization of the rectilinear motion of a single-axle trailer on roads of various longitudinal profiles. 1 cl, 4 dwg.