A braking system for a motor vehicle includes a hydraulic service brake for braking the motor vehicle in driving operation, an electric parking brake for holding the motor vehicle at a standstill, and an electronic control system for automatically controlling the parking brake and the service brake. The electronic control system may be adapted to activate the parking brake, with the service brake activated, after the motor vehicle has been braked to the standstill via the activated service brake, and to at least partly deactivate the activated service brake after the parking brake has been activated. The electronic control system may also be adapted to deactivate the activated parking brake following operation of an accelerator pedal of the motor vehicle.