Abstract: A dampening unit for an offset printing machine, includes a roller pair consisting of a metering roller, and a dampening form roller for applying dampening medium to a plate cylinder of the printing machine, the metering roller and the form roller being in mutually pressing engagement at a first contact zone along respective axially parallel lines on respective casings of the roller pair, a gear drive for driving the roller pair with circumferential speeds of the metering roller and the form roller substantially in a downward direction in vicinity of the contact zone, and means defining a storage space for dampening medium located above the contact zone and including surfaces of the casings of the roller pair and sealing elements located at respective ends of the roller pair, only the metering roller of the roller pair being driven by a gear meshing with a drive gear of the gear drive, the form roller being in driven engagement via friction contact at the first contact zone in a first position of the form rol