Abstract: A device for clamping tools, such as a shank-end mill, comprises an adjusting nut having a bore for receiving and actuating an adapter sleeve for mechanical clamping of the tool. The adjusting nut has at least one pressure medium chamber accommodating a piston and opening into the bore where it is sealed by means of a membrane adapted to rest against the adapter sleeve. A complementary nut is mounted on said adjusting nut for displacing said piston within said chamber, thereby to effect pressure medium-controlled, complementary clamping of the tool.