Goal. To explore theoretically and experimentally the increase of stability of the pivot connection of the technological and power modules of a new design of the modular machine-tractor unit. Methods. Theoretical studies were carried out using the main provisions of the higher mathematics, theoretical mechanics, theory of automatic control. Experimental studies were carried out in field conditions on a real modular machine-tractor unit. Results. The new construction of the pivot connection of the technological module with the power module (tractor) of the modular machine-tractor unit is developed. To ensure satisfactory maneuverability of technological module when cornering it is equipped with vertical and horizontal joints. Limitation of turning ability of technological module relative to the power one in the horizontal plane through this vertical hinge is provided by a hydraulic cylinder, which over-and underpiston cavities are connected through a restrictor with the coefficient of hydraulic resistance at the level of 1.03×106 N•m•s•rad-1. Based on the equivalent power circuit, a mathematical model was created of movement of the unit, allowing to investigate theoretically its stability. As the energizing impact was taken the turning moment, created by external forces. Output parameters of the model were the angle of rotation of the technological module relative to the energy in the horizontal plane, and the heading angle of the latter. The theoretical study is confirmed experimentally. Conclusions. As a result of mathematical modeling, the change of speed of the unit from 2 to 5 m•s-1 does not lead to a deterioration of the stability of motion, neither technological nor, especially, the power modules. The values of the coefficients of resistance of the introduction of wheel tires of power module do not affect its development of fluctuations of the energizing moment. However, the value of the coefficient of resistance of the introduction of the tire of each wheel of the technological module of modular traction vehicle should be not less than 160 kN•rad-1.