The invention is based on a drive device for a movable part, especially a mold closure device for an injection molding machine. A conventional mold closure device possesses a hydraulic cylinder-and-piston unit having a first hydraulic piston, which borders with a first active surface on a first pressure chamber and with a second active surface, which is smaller than the first active surface and faces in the opposite direction thereto, on a second pressure chamber, and comprises a further hydraulic piston, which is fixedly connected to the first hydraulic piston, and possesses a third active surface, which borders on a third pressure chamber and is active in the same direction as the second active surface. Via a valve arrangement, the second pressure chamber can be connected to the first pressure chamber and can be relieved of pressure separately from the first pressure chamber. In the conventional mold closure device, the cylinder-and-piston unit for closing and opening the mold is operated in open hydraulic circuits, the pressure chambers being connected to a tank at the end of the closure operation and at the end of the opening operation and the movable part evidently being braked only by friction. It is an object of the invention further to develop a drive device of the conventional type so that it can be operated at higher dynamics. This is achieved in that a second hydraulic cylinder-and-piston unit is present, having a second hydraulic piston which is movable relative to the cylinder by a drive motor, especially an electric drive motor, and borders with a fourth active surface on a fourth pressure chamber, which is permanently connected to the third pressure chamber, and with a fifth active surface, which faces in the opposite direction to the fourth active surface, borders on a fifth pressure chamber, which can be connected to the first pressure chamber, and wherein the dimensional relationship between the fifth active surface and the difference between the first active surface and the second active surface is equal to the dimensional relationship between the fourth active surface and the third active surface. In a drive device according to the invention, a pressure which brakes the movable part builds up in the first pressure chamber and in the second pressure chamber or third pressure chamber when the second hydraulic piston is no longer moving, without a valve having to be actuated for that purpose.