Recently, rapid development of controlled traffic farming convincingly demonstrates the broad prospects of using the wide span tractor-based field machines throughout the world. The issue at hand lies in the fact that having a wide span tractor-based machine with steering-wheel system moving along the tracks of a constant technological track is not a rational option. According to the concept of bridge and rutting agriculture, it is advisable to subordinate the automated means of mechanization to the principles of the functioning of the coordinate transport system in which machines can move only in two mutually perpendicular directions and for implementation of which the field must have strictly defined dimensions. Therefore, a method of power steering similar to a crawler tractor (track-type tractor) can be more efficient in the automatic driving of bridge means of mechanization within the coordinate-transport system than a kinematic control. Furthermore, methodology utilized for selection of design schemes, parameters and operating modes of machine-tractor aggregates can not be used for study of dynamics of the wide span tractor-based field machine. Theoretical study is based on theoretical mechanics, theory of mobile energy facilities, statistical dynamics and theory of automatic control of linear dynamical systems with reproduction of statistically random control and disturbing input effects. Purpose of the research lies in development of a dynamic model of plane parallel motion in the horizontal plane of a wide span tractor-based field machine unit using a power (onboard) method of control, which would allow investigation of impacts of the control parameters and disturbing influences on the controllability and stability of its motion. Mathematical models have been developed and new regularities of the straightforward parallel movement of the wide span tractor-based field machine unit for controlled traffic farming have been obtained. The results obtained allow the validation of new schemes, design parameters and modes of operation with acceptable controllability and stability of movement in the horizontal plane with a power control method of the chassis.