To control a brake slip control apparatus, the rotational behavior of the wheels or of the axles is sensed with the aid of sensors, and the sensor signals for the generation of valve control signals, by which the braking pressure at the wheels is controlled dependent upon the wheel rotational behavior, will be processed electronically. On the basis of these sensor signals, valve control signals will be produced in at least two independently acting, synchronously driven logical circuit units, which may be integrated circuit configurations or complete "microcontrollers" or single-chip-microcomputers, and the signals' waveforms of each of the two circuit units can be compared and checked for agreement externally and internally at corresponding locations within the two circuit units. Upon the occurrence of variations in the external and/or the internal signals or in the signals' waveform, there will be caused, initiated or prepared a complete or partial disconnection of the brake slip control. A circuit configuration for implementing this method comprises a synchronizable astable multivibrator to process the sensor signals, a valve driver circuit including a level adjusting circuit as well as monitoring circuits for disconnecting the current supply for the regulator and for blocking the valve drivers in the event of interferences or variations in the signals' waveform occurring within the two circuit units. The monitoring circuits, one for each of the two circuit units, act on at least one transistor connected in series in the exciter circuit of a relay, by which the current supply is established or interrupted.