A clamping system for fastening a cooling unit on a circulating supporting element of a caterpillar-type casting machine includes at least one connecting element, which is pre-tensioned in its longitudinal direction by a spring, and a clamping arrangement, by which the cooling unit is fastenable on the supporting element. The connecting element is accommodated in a displaceably mounted manner in the direction of its longitudinal axis inside the supporting element. The clamping arrangement is formed by a head on an upper end face of the connecting element and a recess, which is provided on/in the cooling unit and is brought into interaction therewith. The connecting element is pre-tensioned by the spring toward the supporting element and is transferred into a clamping position, in which the cooling unit, when the head of the connecting element engages with the recess provided on/in the cooling unit, is automatically clamped with the supporting element.