Modern public transport systems are increasingly seen as an important means of promoting the safe mobility of the population, especially in urban areas suffering from growing traffic jams. The Transitway or the new bus system “Bus Rapid Transport” (BRT) is the result of the development of a bus public transport network. In comparison with the subway, this project has obvious advantages: lower cost of network creation, lower cost of rolling stock, mobility, etc. These advantages are manifested, first of all, with the maximum use of passenger capacity of transitways, that is, with the application of three-axles transitways and with their motion on the maximum possible speeds. The purpose of this paper is to present the findings of the transitway motion stability research, which was based on the analysis of solutions of motion differential equations. These equations were compiled with respect to the variables of the longitudinal and transverse velocities of the center of the bus mass and the angular velocities of the bus and of two couplings. As a result of the research, the critical velocity of the three-axles transitway has been determined and factors influencing its numerical value have been analyzed. It has been shown that during the operation of the transitway it is necessary to maintain such pressure in the tires so that, for the selected load on the wheels of the axes of the auto-train, the coefficient of resistance to the lateral separation of the wheels of the steered wheels of the bus and the trailer is smaller than the wheels of uncontrolled axes. The practical value of the research is that this finding will be used for increasing the critical speed vcr of the auto-train.