To enhance variable speed performance of a slide in a slide driving device, improve high response and speed increasing, miniaturize it and reduce the cost thereof.

A regulating device 10 for keeping oil pressure constant is provided in a double tilting and rotating variable displacement pump-motor 8 to be connected to the driving shaft of a press, operated so as to supply a required pressure oil while keeping constant pressure when the pump-motor 8 acts as a hydraulic pump, and operated so as to keep the discharging pressure oil constant when the pump-motor 8 acts as a hydraulic motor. The amount of tilting and rotating of the pump-motor 8 is varied with the tilting and rotating command of a press controller 15, and a slide 3 is driven with driving torque caused in a driving shaft 7 according to the pressure of pressure oil and the amount of tilting and rotating in the pump-motor 8. Also, the regulating device for keeping oil pressure constant is composed of a hydraulic accumulator and the constant oil pressure discharging device.