The embossing device includes—a first path for a first ply of web material; —along the first path, a first embossing roller provided with embossing protrusions; —a first heating device associated with the first embossing roller to heat the surface of the first embossing roller; —at least a first functional roller adapted to perform an action on a ply of web material. The first functional roller is provided with a rotation arrangement, adapted to keep the first functional roller in rotation during a temporary stoppage of the embossing device, with the first functional roller spaced from the first embossing roller and with the first ply of web material stationary in the first path.