A timing belt tensioning device comprising a fixed structure having a spring pressed pivoted structure mounted thereon for pivotal movement about a first axis between first and second limiting positions. The pivoted structure carries a timing belt engaging pulley for rotational movement about a second axis parallel with the first axis. A one-way clutch mechanism is provided for permitting pivotal movement of the pivoted structure in a direction toward a second limiting position and for limiting the pivotal movement of the pivoted structure in an opposite direction toward the first limiting position beyond a predetermined distance measured from the nearest position of the pivoted structure to the second limiting position. The predetermined distance has a maximum dimension such as to prevent loosening of the timing belt engaged by the pulley sufficient to allow disengagement of a tooth thereof with a tooth of a timing pulley and a minimum dimension such as to accommodate normal operating low amplitude movements and thermal expansion during operation. A damping system is provided for damping the operating movements of the pivoted structure permitted by the one-way clutch mechanism.