Abstract: A tensioner has rolling members disposed between a rotatable outer member and a fixed inner member. The inner member has a bottom wall at at least one end thereof. The bottom wall has therein an eccentric position aperture for position adjustment situated at a position deviated from the axis of the inner member. A fixing bolt extends through said aperture. A spring member having at least one end which can be restrained by the inner member and the other end which can be restrained by the restraining portion of a support member to which the tensioner is mounted is provided within the inner member. Thus, a desired tension may be imparted to a transmission strap contacting the outer member by the spring member.