An internal clamping arrangement having a base with a clamping mandrel that extends in a main extent direction and has a guide face and at least two clamping sleeves. The clamping sleeves are displaceable in the main extent direction and are pushed onto the guide face of the clamping mandrel from the direction of a distal end of the clamping mandrel. The clamping sleeves have a clamping portion which can be expanded by displacement, and the outside of which has a clamping face for a respective one of the workpieces. The internal clamping arrangement has at least three piston chambers which act between the base and the at least two clamping sleeves and between the clamping sleeves.