A tire assembly for a two-wheeled vehicle includes tires to be equipped on front and rear wheels, respectively. Each of the tires includes a carcass layer of organic fiber cords arranged at angles of substantially 80.degree. for the front wheel tire or 90.degree. for the rear wheel tire, and a belt layer of organic fiber cords arranged at angles of 5.degree. to 35.degree.. The belt layer of each of the tires consists of inner, intermediate and outer layers. With the front wheel tire, a width of the intermediate layer is narrower than that of the inner layer to form a step of substantially 10 mm on one side and a width of the outer layer is narrower than that of the intermediate layer to form a step of substantially 30 mm on one side. On the other hand, with the rear wheel tire, a width of the intermediate layer is wider than that of the inner layer and a width of the outer layer is wider than that of the intermediate layer to form steps of substantially 7 mm successively at one sides of the respective layers.