The invention relates to a hydraulic drive for a punch or forming machine comprising a working cylinder (2) with several pressure chambers (6, 8), the plunger (4) of said cylinder acting directly or indirectly on a workpiece to be machined. To retract or extend the plunger (4), at least one pressure chamber (6) of the working cylinder (2) is subjected to a replenishment pressure or a supply pressure by means of a constantly adjustable valve (10). Said drive also comprises a valve assembly (26), which is connected upstream of the constantly adjustable valve (10) and is used to subject the inlet connection (E) of the constantly adjustable valve (10) to a higher or lower supply pressure. Said valve assembly (26) has a selector valve (26), which depending on the load pressure on the working cylinder (2), can switch between an original position and a selector position in order to tap the supply pressure from a low-pressure source (ND) or a high-pressure source (HD).