A rotation transmission device comprising an input shaft, an output shaft arranged coaxial with the input shaft, a two-way clutch configured to selectively transmit torque between the input shaft and the output shaft, and an electromagnetic clutch configured to selectively engage and disengage the two-way clutch, wherein the two-way clutch comprises: an outer ring provided at an end of the output shaft; an inner ring provided at an end of the input shaft; a control retainer and a rotary retainer which both have bars (25, 29) disposed between an inner periphery of the outer ring and an outer periphery of the inner ring and arranged such that the bars of the control retainer circumferentially alternate with the respective bars of the rotary retainer, with pockets defined between adjacent ones of the bars (25, 29) of the control retainer and the rotary retainer; a plurality of pairs of engaging elements, each pair of the engaging elements being mounted in one of the pockets so as to be engageable with the inner periphery of the outer ring and the outer periphery of the inner ring; and elastic members mounted in the respective pockets and biasing the respective pairs of engaging elements away from each other, wherein the electromagnetic clutch comprises an armature coupled to the control retainer, a rotor facing the armature in an axial direction, and electromagnet facing the rotor in the axial direction and configured to attract the armature against the rotor, thereby moving the control retainer in the axial direction toward the rotor, upon energization of the electromagnet, wherein the two-way clutch further comprises a motion converter mechanism configured to convert the axial movement of the control retainer toward the rotor to relative rotation between the control retainer and the rotary retainer in a direction in which circumferential widths of the pockets decrease, and disengaging the engaging elements, characterized in that the rotation transmission device further comprises an anti-rotation means disposed between the outer ring and the control retainer and configured to prevent relative rotation between the outer ring and the control retainer while the electromagnet is de-energized and the two-way clutch is engaged, so that a flange of the control retainer is in contact with an open end surface of the outer ring. an outer ring provided at an end of the output shaft; an inner ring provided at an end of the input shaft; a control retainer and a rotary retainer which both have bars (25, 29) disposed between an inner periphery of the outer ring and an outer periphery of the inner ring and arranged such that the bars of the control retainer circumferentially alternate with the respective bars of the rotary retainer, with pockets defined between adjacent ones of the bars (25, 29) of the control retainer and the rotary retainer; a plurality of pairs of engaging elements, each pair of the engaging elements being mounted in one of the pockets so as to be engageable with the inner periphery of the outer ring and the outer periphery of the inner ring; and elastic members mounted in the respective pockets and biasing the respective pairs of engaging elements away from each other, wherein the electromagnetic clutch comprises an armature coupled to the control retainer, a rotor facing the armature in an axial direction, and electromagnet facing the rotor in the axial direction and configured to attract the armature against the rotor, thereby moving the control retainer in the axial direction toward the rotor, upon energization of the electromagnet, wherein the two-way clutch further comprises a motion converter mechanism configured to convert the axial movement of the control retainer toward the rotor to relative rotation between the control retainer and the rotary retainer in a direction in which circumferential widths of the pockets decrease, and disengaging the engaging elements, characterized in that the rotation transmission device further comprises an anti-rotation means disposed between the outer ring and the control retainer and configured to prevent relative rotation between the outer ring and the control retainer while the electromagnet is de-energized and the two-way clutch is engaged, so that a flange of the control retainer is in contact with an open end surface of the outer ring.