An apparatus and a process for closed loop control of a motion quantity representing the vehicle motion which means determine the yaw rate of the vehicle, the longitudinal speed of the vehicle, and the transverse acceleration of the vehicle. Moreover, the apparatus influences the forward moment and/or the braking moment of individual wheels of the vehicle. The apparatus further determines a transverse acceleration component dependent on the roadway transverse inclination, as well as correcting the transverse acceleration of the vehicle at least as a function of the transverse acceleration component dependent on the roadway transverse inclination. The determination of the transverse acceleration component dependent on the roadway transverse inclination and also the correction of the transverse acceleration of the vehicle as carried out in a stable state of the vehicle characterized by the yaw rate and the transverse acceleration.