Processing apparatus for processing continuous web material, said apparatus comprising: - a first conveying device comprising a first inlet, a first outlet and an endless slidable first flexible element, said first flexible element being arranged for conveying continuous web material from said first inlet to said first outlet, said first flexible element being configured with variable geometry that is controlled so as to vary at least the position of said first outlet; - a processing unit arranged near said first outlet for receiving continuous web material from said first conveying device, said processing unit being drivable between at least one engagement position in which it engages the continuous web material and at least one disengagement position, said processing unit being movable together with said first outlet; characterized by - control means configured to control in a coordinated manner the sliding of said first flexible element, the drive of said processing unit and the movement of said processing unit together with said first outlet, to perform a processing cycle in which the continuous web material advances in a continuous manner in a forward direction, wherein said processing cycle comprises at least one forward step in which said processing unit advances in said forward direction together with said first outlet and at least one return step in which said processing unit goes back in the opposite direction together with said first outlet, wherein said processing unit assumes said engagement position during at least a part of said forward step to engage the continuous web material as it advances with the same material, wherein said processing unit assumes said disengagement position during at least a part of said return step. - a first conveying device comprising a first inlet, a first outlet and an endless slidable first flexible element, said first flexible element being arranged for conveying continuous web material from said first inlet to said first outlet, said first flexible element being configured with variable geometry that is controlled so as to vary at least the position of said first outlet; - a processing unit arranged near said first outlet for receiving continuous web material from said first conveying device, said processing unit being drivable between at least one engagement position in which it engages the continuous web material and at least one disengagement position, said processing unit being movable together with said first outlet; characterized by - control means configured to control in a coordinated manner the sliding of said first flexible element, the drive of said processing unit and the movement of said processing unit together with said first outlet, to perform a processing cycle in which the continuous web material advances in a continuous manner in a forward direction, wherein said processing cycle comprises at least one forward step in which said processing unit advances in said forward direction together with said first outlet and at least one return step in which said processing unit goes back in the opposite direction together with said first outlet, wherein said processing unit assumes said engagement position during at least a part of said forward step to engage the continuous web material as it advances with the same material, wherein said processing unit assumes said disengagement position during at least a part of said return step.