This paper focuses on a concept, direct effect, which has been at the heart of Marc Maresceau's own intellectual journey, the subject of his own PhD, later turned into a marvellous monograph which continues to repay close study. It explores, prospectively, what the status of the Convention in EU law could, and should be, once the EU has become a Contracting Party. The paper does so, at one level, on the basis of the existing principles regarding the effects which international agreements have in the EU legal order. It analyses the scope of the ECJ's jurisdiction to interpret and apply the Convention, once it is concluded. The paper examines the potential legal effect of the Convention in EU law. It analyzes the following question: what will be the effect of judgments of the ECtHR in the EU legal order?  Keywords: ECtHR, EU legal order, European Convention on human rights, Marc Maresceau