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The wheels of decelerating vehicles in braking mode roll with increased slip, up to complete lock-up, which is a negative phenomenon. This is effectively managed by the anti-lock braking system (ABS). However, in the course of braking, especially before the system activation, self-excited oscillatory processes with high amplitudes may occur, causing increased dynamic loads on the drive system. The paper studies the braking processes of a vehicle with an electromechanical individual traction drive in both electrodynamic regenerative and combined braking modes, utilizing the drive and the primary braking system. The theoretical framework is provided for identifying the self-excited oscillation onset conditions and developing a technique to detect wheel slips during braking to suppress these oscillations. To check the functionality of the wheel-slip observer in braking mode, the performance of the self-excited oscillation pulse suppression algorithm was studied in the MATLAB Simulink 2018b software package. The study results can be used to develop control systems equipped with the function of suppressing self-excited oscillations by vehicle motion. [ABSTRACT FROM AUTHOR]