The powers of supervision and enforcement of due diligence obligations, other than the additional obligations to manage systemic risks imposed on providers of very large online platforms and of very large online search engines by this Regulation, should be shared by the Commission and by the national competent authorities. On the one hand, the Commission could in many instances be better placed to address systemic infringements committed by those providers, such as those affecting multiple Member States or serious repeated infringements or concerning a failure to establish effective mechanisms required by this Regulation. On the other hand, the competent authorities in the Member State where the main establishment of a provider of very large online platform or of very large online search engine is located could be better placed to address individual infringements committed by those providers, that do not raise any systemic or cross-border issues. In the interest of efficiency, to avoid duplication and to ensure compliance with the principle of ne bis in idem, it should be for the Commission to assess whether it deems it appropriate to exercise those shared competences in a given case and, once it has initiated proceedings, Member States should no longer have the ability to do so. Member States should cooperate closely both with each other and with the Commission, and the Commission should cooperate closely with the Member States, in order to ensure that the system of supervision and enforcement set up by this Regulation functions smoothly and effectively.