A steering apparatus for vehicles which includes a pinion rotatably mounted on an arm movable longitudinally in response to turning movement of a steering wheel, and a pair of longitudinally movable racks held in meshing engagement with the pinion. One of the racks is operatively coupled with front wheels of the vehicle and with a pivot arm pivotable on a movable pivot which is displaceable along the pivot arm in response to vehicle speeds. The other rack is coupled through a pivotable lever with an arm which is pivotally mounted on the pivot arm and is operatively coupled with the rear wheels. When the steering wheel is turned, the front and rear wheels are turned in the same direction or in opposite directions, depending on the position of the movable pivot on the pivot arm, which position is a function of the vehicle speed. The front and rear wheels are turned in the same direction when the vehicle is running at a high speed, and in opposite directions when the vehicle is running at a low speed. The racks and pinion may be dispensed with and the front wheels operatively coupled only through a connecting rod pivotally connected to a pivot arm pivotally mounted on a movable pivot, the rear wheels being pivotally connected through an arm to the pivot arm.