Abstract: On-machine supercalender apparatus is provided at the output side of a paper machine and includes a plurality of soft and hard calendering rolls defining a plurality of soft calendering nips arranged successively in the direction of the run of the web being calendered, each soft calendering nip being formed by a pair of calendering rolls including a respective soft calendering roll and a corresponding respective hard calendering roll. According to the invention, the run of the web is guided successively through the nips in a manner such that the soft rolls do not participate in the guidance of the run of the web, i.e., the web is only guided in its run on the outer surfaces of the hard calendering rolls and, possibly, guide rolls.