A tool holder for a punching machine, comprising several punching units (14) that are accommodated in tool holding fixtures (12) in the holder (10) in addition to gas pressure springs (15) to recall the punches (20). The advantage of gas pressure springs is that the pressure level can be adapted to the material that is to be machined. In order to make it easier and quicker to achieve said adaptation, the pressure chambers (28, 32) of the gas pressure springs are joined to a common supply line (44) which can be connected to a pressure gas source. As a result, it is possible to change the internal pressure of all the gas pressure springs (15) at the same time.