An analysis of the operating conditions of the traction drives of an electric rolling stock with asynchronous traction motors was conducted. In the process of operation, the electric traction drive with both direct torque control and vector control was found to possibly experience unstable modes, both in terms of power supply and load. The models of electric locomotive traction drives with asynchronous electric motors with either vector or direct torque control were adapted to account for the possible presence of the aforementioned operational factors. As a result of the modeling, the starting characteristics of the electric traction drives with different control systems were obtained both in the absence and in the presence of power supply and load disturbances. The following cases were investigated for the drive with vector and direct torque control in the absence of power supply and torque disturbances: drive output at the rated speed of rotation of the electric motor shaft; 10% reduction in the rated speed; 10% increase in the rated speed. The comparison of the results obtained has demonstrated that, at lower than nominal frequencies, the electric traction drive with direct torque control has higher accuracy in its regulation of the rotational speed and torque, lower power consumption from the power supply, lower torque overshooting, but a higher level of torque pulsations than the electric traction drive with vector control. Meanwhile, at higher than nominal frequencies, the vector control has higher accuracy in its regulation of the speed, lower torque overshooting, shorter duration of transient processes, and lower torque pulsations than the direct torque control. Moreover, as a result of the investigations, the traction drive with direct torque control has been found to be more resistant to power supply and load disturbances. The results of this work are applicable to the investigation of the influence of electric traction drive control methods on the energy efficiency of the traction drive of an electric locomotive with an alternating current (AC).