An apparatus for mounting semiconductor chips has a pick and place system arranged stationary in vertical direction for the picking, transport and placement of a semiconductor chip onto a substrate. The pick and place system comprises a bondhead with a chip gripper deflectable relative to the bondhead. The deflection of the chip gripper takes place by means of a pneumatic drive arranged on the bondhead which has two pressure chambers separated by a piston, whereby the chip gripper is secured to the piston. The pressure p.sub.1 prevailing in the first pressure chamber and the pressure p.sub.2 prevailing in the second pressure chamber are dynamically controlled by means of a regulator controlled valve system. The regulator can be operated in two operating modes. In the first operating mode, the deflection of the chip gripper and/or a variable derived from it is controlled based on the signal delivered by a position encoder which measures the deflection of the chip gripper. In the second operating mode, the pressure p.sub.1 and/or the pressure p.sub.2 and/or the pressure differential p.sub.1-p.sub.2 is controlled.