In a dampening unit for offset printing machines having a dampening-medium tank, a rotating screen cylinder formed of a perforated support member covered by a blanket for conveying dampening medium supplied thereto from the tank, and a blow tube located adjacent the blanket and formed with nozzle openings for spraying the dampening medium by means of blowing air from the blanket onto a dampening unit roller, the improvement therein which includes means for freely rotatingly guiding the screen cylinder, and a driven dampening-medium conveying roller immersed in the dampening medium received in the tank and being in frictional engagement with the screen cylinder so as to feed the dampening medium from the tank to the blanket.