The rubber surface of a smoother roll in a paper-making machine is deformed into a certain convex polygon at a high nipforce and a an operating speed at which the rotating rolls are in contact with each other. This paper describes the theoretical analysis and the numerical computational results taking the viscoelastical deformation of the rubber surfaces of a pair of rolls into account, regarding this vibration phenomenon as instability due to the time lag. The authors found from the numerical calculation that (1) the influence of the rotating speed of rolls and the rigidity of the roll supports on the stability is the same as that for the case treated in the previous report, in which one of two rolls does not deform ; (2) this instability phenomenon tends to occur as the hardness of the opposite roll increases ; and (3) the unstable regions are classified into two types according to differences between roll diameters.