Concurrent criminal jurisdiction depicts a scenario where two or more judicial systems have the legal capacity to investigate, prosecute and punish an accused person for the same criminal acts under their respective, separate jurisdiction. This usually occurs between sovereign states. In the realm of crimes under international law, the distinguishing characteristic is the universal jurisdiction that is conferred on all States to prosecute and punish the perpetrators of such crimes. The "cumulative effect of these different principles of jurisdiction sometimes is to vest multiple states with concurrent jurisdiction to prosecute a given crime. This paper would attempt to analyze the concept of primacy that governs the concurrent jurisdiction model between the two ad hoc ICTY and ICTR on the one hand, and national judicial systems; and the concept of complementarity, which governs concurrent jurisdiction between the ICC and national courts. In both cases, reference shall be made to the concept of state sovereignty and the leverage it still has in international law, albeit the transition to globalization and supranationalism. Most of the case studies will refer to the ad hoc ICTY and ICTR because they are functional. The ICC is still to come into existence, thus its analysis shall be based on hypothesis.