The present invention provides a rotation-transmitting apparatus with a built-in one-way clutch which is capable of preventing rolling contact surfaces and rolling surfaces of inner and outer rings of a rolling bearing frompeeling and fretting wearing and is excellent in its resistance to heat and wear. The rotation-transmitting apparatus with a built-in one-way clutch has an inside rotational member; a cylindrical outside rotational member disposed concentrically with the inside rotational member; a one-way clutch connecting the outside surface of the inside rotational member and the inside surface of the outside rotational member to each other only when the outside rotational member rotates at a higher speed than the inside rotational member; and a pair of rolling bearings allowing the inside rotational member and the outside rotational member to rotate relative to each other. Grease is enclosed inside an internal space of a clutch where a plurality of rollers is mounted and inside a space of the bearing where a plurality of rolling elements is mounted. The grease contains a base oil, a thickener, and an additive. The base oil is PAO oil. As the additive, 0.01 to 15 wt% of at leas one compound selected from among ZnDTC and ZnDTis contained for the entire amount of the grease.