A novel control device for a vehicle power steering apparatus or system is improved for providing preferable steering convergnecy even under the execution of VSC, while ensuring the steering smoothness under normal running conditions. In the control device, the target value of total modification torque to be added to steering torque through an power steering apparatus, is calculated based upon steering assist torque, calculated based upon at least steering torque; steering converging torque, based upon a steering velocity; and behavioral deterioration-suppressing torque for suppressing unwanted steering motions which would cause further deterioration of a vehicle behavior under oversteered or understeered conditions. In this calculation, when a predetermined condition is satisfied, the degree of contribution of the target value of the behavioral deterioration-suppressing torque to the target value of the total modification torque is rendered higher than the degree of contribution of the target value of the steering converging torque to the target value of the total modification torque.