In vehicular running apparatus and method, a yaw rate target deceleration calculated on a basis of a yaw rate and a preset lateral acceleration set value is compared with a navigation target deceleration calculated on a basis of a target vehicle speed calculated on a basis of a state of a curved road located in front of a running road on which the vehicle is running and the preset lateral acceleration to select a target deceleration from one of the yaw rate and navigation target decelerations which is lower than the other and a target vehicle speed command value is calculated on a basis of the selected target deceleration, the calculated vehicle speed command value being outputted to decelerating means of the vehicle.