A process for drying a paper web and a drying section of a paper making machine. The drying section includes at least one drying group comprised of a plurality of drying cylinders, each at least partially wrapped by a web to be dried. The drying cylinders having peripheral surfaces heated for drying the web moving therepast. The peripheral surfaces of the drying cylinders in the drying groups are rotated at the velocity of the web along the web path. At least one of the drying cylinders in at least one drying group is driven to rotate at a speed that is different than the speed of the web moving past the at least one cylinder. The at least one cylinder may be selectively driven to rotate faster or slower than the speed of the web moving therepast, which applies more heat to the paper web. The invention is adaptable for a single tier drying section and/or for a double tier drying sections or for other drying section arrangements. The operation of a drying cylinder at a different speed than the other cylinders is useful for one or more than one drying cylinder in a drying group and where a drying section is comprised of more than one drying group, is useful for a drying cylinder in one or more of the drying groups.