Abstract: The adoption of the Digital Markets Act (DMA) has changed the regulatory landscape for the digital sector in Europe and beyond. The DMA amounts to a complete system of ex ante rules that provide for a specific clausus numerus of obligations and prohibitions and aims at fostering contestability and fairness in the area of large digital platforms. The DMA is ostensibly not competition law, since it functions ex ante and not ex post, but in reality, it is very much influenced by competition law and, therefore, is very much seen as the ex ante side of the same coin, the other side of the coin being the ex post competition rules. Like in competition law, the question of private enforcement takes a central role in the overall system of enforcement. The purpose of the present article is to shed light on the private enforcement of the DMA rules. In particular, it deals, first, with the preliminary question, i.e. that the enforcement of the DMA is not restricted to public authorities (the European Commission) but is also enforced by the courts in civil law disputes between private parties. Second, it considers the questions of available remedies in private enforcement, the applicable procedural rules and the rules on jurisdiction and conflict of laws (private international law). Finally, it centres on risks of fragmentation and the DMA mechanisms to remedy this problem.