The work is based on the International Court of Justice's judgment of February 3rd, 2012, in the Jurisdictional Immunities case between Germany and Italy concerning the jurisdictional immunities of a State before national courts of another State. One of the arguments of Italy against the granting of immunity to Germany before national courts was that in cases of violations of international humanitarian law, which constitute violations of jus cogens law, reparation imperatively has to be made by the wrongdoing State. This work generalizes Italy's argument to all jus cogens obligations and discusses the legal nature of the obligation to make reparation arising out of the breach of such a jus cogens obligation. Is the obligation to make reparation a jus cogens norm on itself? This interesting question mixes aspects of the natural law doctrine, of State responsibility and of the effects of jus cogens. This work discusses this question and tries to find out if, in the actual state of public international law, the obligation to make reparation for the breach of a jus cogens obligation has jus cogens character as well.