The cases in which the arbitrators deny their jurisdiction are rare. Nevertheless, they exist and tend even to multiply, arbitrations proceedings becoming more and more complex. The famous Abela case is an illuminating example. In the examined scenario, the arbitrators make an award, called negative award on jurisdiction (sentence d’incompétence). The qualification of award was certainly able to be disputed: how could the arbitrators make a jurisdictional decision in presence of a lack of jurisdiction? However, in French law, as in other laws, the qualification of award is completely admitted, the principle of competence-competence justifying the power of the arbitrators to affirm or deny their jurisdiction. It ensues from it certain number of consequences. Among them, there is the res judicata effect accompanying the negative award on jurisdiction. Complex by nature, the res judicata question of arbitral awards is even more complex in presence of a negative award on jurisdiction. As quite other award, this type of award can be also challenged in order to set it aside. What are the grounds for setting aside? What is the extent of the control? In French case law, the control is total. In this perspective, it is possible to set aside an award if the arbitrators denied erroneously their jurisdiction. The consequences of such an annulment are problematic. Is it necessary to appoint in that case a new arbitral tribunal? Do the appointed arbitrators have to conform to the decision and so accept inevitably their jurisdiction? The topic opens on many new questions and shows the contemporary evolution of arbitration law, which becomes a discipline more and more technical and complex.