A rotation transmission device includes a two-way clutch which is selectively engaged and disengaged by an electromagnetic clutch. The two-way clutch includes a control retainer and a rotary retainer. The control retainer and the rotary retainer have flanges and bars formed on outer peripheral portions of the respective flanges and arranged so as to circumferentially alternate with each other with pockets defined between adjacent bars. Two rollers are received in each pocket. When the control retainer and the rotary retainer are rotated relative to each other, the rollers are adapted to be pushed by the bars to the disengaged position. An anti-rotation arrangement is provided on opposed surfaces of an outer ring and the control retainer member. The anti-rotation arrangement is adapted to prevent the control retainer from rotating relative to the outer ring while the rollers are in engagement, thereby preventing the rollers from moving to the neutral position.