The invention relates to a drive device, which is used in particular for the closing unit, the injection unit or the ejectors of a plastics injection molding machine and which has a drive element which can be axially moved by an electric motor and a hydraulic unit which, by moving the drive element, can be moved in the same direction as the latter. Drive devices for the stated applications depend on firstly performing a rapid positioning movement and then exerting great forces. In the case of a known drive device with the stated features, the hydraulic unit is a hydraulic cylinder, which is displaced during the positioning movement by the electric motor via a lifting spindle and to which pressure medium is supplied via a valve for the exertion of a great force. In the case of this known drive device, apart from the electrical installation, a complete hydraulic system is also necessary. Furthermore, great forces of reaction act on the lifting spindle. This is avoided if, according to the invention, the hydraulic unit is a force multiplier with two pistons, which can be moved in relation to one another and differ in the size of their effective surface areas, and an intermediate part, which together with the pistons encloses a pressure chamber filled with a pressure fluid, if the small piston, having the smaller effective surface area, is mechanically connected to the drive element, if the hydraulic unit as a whole can be moved for the positioning movement and if the intermediate part can be blocked against displacement in relation to a fixed frame for the exertion of a great force by the large piston, having the greater effective surface area.