A spinal column stabilization system comprising at least one first bone attachment device, at least one second bone attachment device and a connecting element, which connecting element comprises a first attachment section for fixing to the at least one first bone attachment device, a second bone attachment section for fixing to the at least one second bone attachment device and an at least partially flexible intermediate section that is arranged or formed between the first and the second attachment section, which intermediate section is in the form of a strip-like, winding leaf spring element and comprises at least one recess which is open to the side in a direction transverse to a longitudinal axis defined by the intermediate section, wherein at least one of the two leaf spring element surfaces of the leaf spring element comprises at least one stiffness-modifying element.