Abstract: A deep boring or drilling mill, especially of the horizontal type, comprises a machine bed. A headstock and a tailsotck are operatively arranged on the machine bed. A cooling medium supply device is operatively arranged between the headstock and the tailstock and participates in or performs a clamping movement. The displacement movements of the headstock and of the cooling medium supply device are synchronized with each other during the clamping phase and during the release phase of these displacement movements. Preferably, the length and speed of the displacement movements are balanced or adjusted by an electrical bridge circuit.