When mounting semiconductor chips, the semiconductor chips are presented on a wafer table where they are picked one after the other by a pick and place system, transported and placed onto a substrate that rests on a supporting surface of a substrate table. The wafer table is aligned diagonally to the supporting surface of the substrate table whereby part of the wafer table is located under the substrate table. The pick and place system comprises a shuttle with a swivel arm carrying a bondhead. The swivel arm is swivelled back and forth between two predetermined swivel positions whereby in the first swivel position a longitudinal axis of the swivel arm embraces the angle .phi. with the perpendicular to the supporting surface of the substrate table and whereby in the second swivel position the longitudinal axis of the swivel arm runs orthogonally to the supporting surface of the substrate table.