Hydraulic drive system associable with a multi-press punching apparatus for operating a plurality of punching tools of said punching apparatus along respective operating axes in a separate and independent manner so as to interact with a workpiece, the hydraulic drive system comprising: - a plurality of hydraulic cylinders, each hydraulic cylinder associable with a respective punching tool and provided with a respective piston that defines a thrust chamber and a return chamber inside the hydraulic cylinder and associable with the corresponding punching tool for moving the latter along the respective operating axis; - a first pump of reversible type connected to said thrust chambers of said hydraulic cylinders and arranged to send oil at a supply pressure (P A) at least in one of said thrust chambers in a driving phase so as to push the respective piston along a working direction and allow the punching tool associable therewith to interact with the workpiece, or to suck oil from at least said thrust chamber in a sucking phase to allow the respective piston moving along a return direction and said punching tool disengaging and moving away from said workpiece; - a plurality of selector valves, each selector valve being associated with a respective hydraulic cylinder, interposed between said first pump and the thrust chamber of the hydraulic cylinder and activable to put into flow connection the first pump with the thrust chamber so as to operate the hydraulic cylinder; - a hydraulic accumulator connected to said return chambers of said hydraulic cylinders and arranged for maintaining in said return chambers oil at a defined preload pressure, in particular for moving along the return direction at least one piston of a hydraulic cylinder operated by activating the corresponding selector valve. - a plurality of hydraulic cylinders, each hydraulic cylinder associable with a respective punching tool and provided with a respective piston that defines a thrust chamber and a return chamber inside the hydraulic cylinder and associable with the corresponding punching tool for moving the latter along the respective operating axis; - a first pump of reversible type connected to said thrust chambers of said hydraulic cylinders and arranged to send oil at a supply pressure (P A) at least in one of said thrust chambers in a driving phase so as to push the respective piston along a working direction and allow the punching tool associable therewith to interact with the workpiece, or to suck oil from at least said thrust chamber in a sucking phase to allow the respective piston moving along a return direction and said punching tool disengaging and moving away from said workpiece; - a plurality of selector valves, each selector valve being associated with a respective hydraulic cylinder, interposed between said first pump and the thrust chamber of the hydraulic cylinder and activable to put into flow connection the first pump with the thrust chamber so as to operate the hydraulic cylinder; - a hydraulic accumulator connected to said return chambers of said hydraulic cylinders and arranged for maintaining in said return chambers oil at a defined preload pressure, in particular for moving along the return direction at least one piston of a hydraulic cylinder operated by activating the corresponding selector valve.