The article is devoted to the theoretical mechanical models of the guided longitudinal motion of a couple of transport units. Such models are essential for analysis and construction of complex transportation system models, since the traffic, in which only the adjacent vehicles are interacting, can be presented as a set of transport units’ couples. The key target is to create and research the models, suitable for the robot-aided vehicles, considering the difference between the piloted, semi-automated and automated control versions. A new approach is introduced for the coupled transport units’ movement, considering velocity, acceleration and the dynamic parameters of the transport units. Absolute motion for a single transport unit model is analyzed, as well as an absolute and relative motion for the coupled transport units’ model. Stability for the suggested dynamical system is tested in terms of Lyapunov and Routh-Hurwitz stability criteria. Motion without harmonic oscillations of the state variables is considered as a comfortable motion mode for the model’s linear approximation. The ways of maintaining the required mode of the coupled movement for different types of control are considered. Limitations for the piloted control mode are determined. The asymmetry of the control options for the leading and following transport units is detected and studied. Models of an absolute and relative motion, suitable for vehicles, are presented. The results of the numerical experiments, proving the presented analytic models, show possible options for different types of traffic control, which ensure a stable coupled movement of the transport units.