The two-phase method is quite widespread when harvesting grain crops and forage grasses. For its implementation, farmers prefer harvesting units with a front-mounted header. The main disadvantage of such units is that after their passage in the space between the swaths of mown crops, open soil falls under the direct influence of sunlight. Subsequently, this leads to an intensive loss of its moisture. A harvesting unit has been designed to eliminate this shortcoming, consisting of a tractor with a front harvester and a soil-cultivating machine (disc harrow) mounted at the rear. The latter chops stubble and soil in the space between the swaths of the mowed crop, contributing to soil moisture conservation. In the diagram plan, the tillage machine can have a swivel or fixed conjunction with the tractor in a horizontal plane. A mathematical model of the harvesting unit plane-parallel movement in the horizontal plane has been designed to choose these conjunctions better. In the study, it is used to analyze the corresponding amplitude (AFC) and phase (PFC) frequency characteristics of a dynamic system when it is working out a control action in the form of the sighting point transverse shift. As a mathematical modeling result, it was found that the fixed conjunction of a tillage machine with a tractor is preferable. In this case, the natural AFC practically approaches the perfect one for servo dynamical systems. The correlation degree between the tractor‘s steered wheels‘ rotation and heading angles increases by almost 37%. As a result, this leads to a significant decrease in this parameter variance fluctuations, which contributes to an increase in the harvesting unit controllability movement as a whole.