The drive for the multicolor rotary press has a main drive shaft, a connected synchronized gear train which extends substantially parallel to the drive shaft and which connects the press mechanisms with each other and a torsion spring-rod which couples the main drive shaft and the synchronized gear train. For coupling the main drive shaft with the synchronized gear train the torsion spring-rod is mounted on an axle journal of a press cylinder. To provide a drive for operation of the press at several different operating speeds a force-locking or frictionally-engaging coupling clutch is mounted on bevel gear shafts located between the press cylinder of one press mechanism drivable by a torsion spring-rod and another press cylinder of an adjacent press mechanism carrying a transversely moving linkage. One of the bevel gear shafts is driven by another gear coupled with the main drive shaft, so that, when the clutch is engaged, particularly at start-up and low speed operation, the press cylinders are driven without the torsion spring-rod, but when the clutch is disengaged, the press cylinders are driven through the torsion spring-rod thus damping oscillations due to gear teeth tolerances.