In a transfer line for the metal-cutting machining of workpieces, the transfer line including a plurality of machining stations arranged one after the other substantially in one plane. The workpieces are arranged in hanging fashion in such a way that clamping devices are arranged above the workpieces, thereby providing a falling and collecting space for the cuttings under the workpieces. Removal of cuttings is thereby facilitated and it is not necessary to flush the cuttings away using large amounts of coolant.