The International Law Commission's decision to maintain Articles 40 and 41 is based on the conviction that serious breaches of peremptory norms entail specific legal consequences within the field of state responsibility. Among these consequences, it is possible to distinguish between (i) specific obligations binding on other states, (ii) specific rights of other states and (iii) specific obligations of the responsible state. This article critically assesses whether international law recognizes specific consequences falling within the third of these categories. It discusses six prominent candidates suggested in international practice, literature, and the work of the ILC — such as the obligations to provide assurances of non‐repetition, to pay punitive or exemplary damages or to prosecute individual perpetrators of serious wrongful acts. The article concludes that none of these candidates qualifies as a specific consequence of serious breaches of peremptory norms — partly because the alleged specific obligation has not been recognized in international law, and partly because it equally applies to internationally wrongful acts that do not constitute serious breaches in the sense of Article 40. It follows that international law at present does not impose specific obligations on states responsible for serious breaches of peremptory norms. This in turn raises doubts as to the viability of the distinction between serious breaches and ordinary wrongful acts.