In a device for assuring the standstill of a motor vehicle having a contained in at least one electronic control unit distance-related longitudinal dynamics control module by which the motor vehicle is decelerated while maintaining a certain distance to a target object to a standstill, at least until reaching the stop of the longitudinal dynamics control module to a brake control module a target braking torque determined. At a defined time after the first stoppage of the motor vehicle is detected, a transfer signal to the brake control module is transmitted from the longitudinal dynamics control module. Then, the brake control module holds regardless of the input of a setpoint braking torque by the longitudinal dynamics control module independently a wheel braking torque in the sense of a parking brake function maintained. At a defined second time after a start command are the longitudinal dynamic control module, beginning with the disposal at that time Istbremsmoment again itself a target brake torque to reduce the Radbremsmoments ago.