A bearing system (15) rotatably supporting a shaft (16) or any other similar machine element is unrotatably fitted in a bearing inserting aperture (41), while at the same time, the bearing system comprises a fixed bushing (48) which is located more adjacently than the shaft (16) to a portion thereof on which external force acts, and is fixed within the bearing inserting aperture (41), a movable bushing (51) which cooperates with the fixed bushing (48) to hold the shaft (16), and is allowed to advance or retreat relative to the fixed bushing (48), and springs (53, 54) which allow the movable bushing (51) to approach the fixed bushing (48). If the outer circumferential surface of the shaft (16) and the inner peripheral surface of the fixed bushing (48) are worn out or abraded, the movable bushing (51) is moved in proportion to the wear or abrasion amounts of the shaft (16) and the fixed bushing (48) in the direction of the fixed bushing (48) by using the springs (53, 54). Therefore, the outer circumferential surface of the shaft (16) and the inner peripheral surface of the bearing system (15) are free from any backlash therebetween, and there is no disadvantage which would result from the backlash.