An electromechanical actuator is integrated into a blackout or sun-shading device that includes a screen, top and bottom bars, and top and bottom winding shafts. The screen is between the bars. The top bar is connected to the top winding shaft by first cords. The bottom bar is connected to the bottom winding shaft by second cords. The electromechanical actuator includes first and second transmission devices and an electric motor that drives the shafts. The first transmission device connects to the motor and the top winding shaft and includes a first clutch. The second transmission device connects to the electric motor and the bottom winding shaft and includes a second clutch. When the motor is activated with only one clutch engaged, only one winding shaft is rotated. Moreover, when the motor is activated electrically and the clutches are engaged, the winding shafts are rotated by the motor.