A connection device has a line portion having, at its end, a radially outwardly projecting abutment flange for abutting against a corresponding abutment flange of a further line portion which is to be coupled to the line portion, and a ring-segment chain comprising a plurality of ring segments connected to one another in a pivotable manner in a common ring plane, wherein the ring-segment ends which form the chain ends can be latched to one another to give a ring-form connection clamp. The line portion is designed in the form of a tubular connection stub with first thread means spaced apart axially from the abutment surface of its abutment flange and in that each ring segment has a radially inwardly projecting clamping flange and second thread means, which are spaced apart axially from said clamping flange and correspond to the first thread means.