Abstract: The present invention concerns a viscous damping device for reducing the rotation speed of the winding roller of a screen once the screen has been previously unrolled from the roller against an energy storing device, which causes the rotation of the roller as the screen is being rewound. According to the invention, the device has a shaft, with a first end having means for axial coupling thereof to the screen winding roller, a rotor, coaxially placed on said shaft, a box-like element enclosing said rotor, as well as means for connecting said shaft to said rotor as the roller rotates and the screen is rewound and for disconnecting said shaft from said rotor as the screen is unwound from the roller.