A rear wheel is provided with a steering characteristic such that a vehicle runs on a cornering path with a longitudinal center line of the vehicle substantially aligned with a tangential line of the cornering path throughout cornering movement. A fail judge device is provided for judging when a rear wheel steering device failure is present in light of a criterion based on a rear wheel steering. A criterion change device is also provided for changing the criterion between a transitional cornering condition, in which the vehicle is in an initial stage of a cornering movement just after a steering operation and before a cornering force acting on the vehicle body reaches a substantial value, and a steady cornering condition, in which the cornering force has reached the substantial value. A reverse phase control can be properly performed without failure judgment. This assures that a desirable driving feeling is provided for the driver when cornering as well as improved safety.