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The substantive competence of international court and the complementary of the national courts is the most important principle that the thought of court has been base on sine it is considered as a deterrent mechanism in the shadow of the globalization of law at the present that is the national jurisdiction should be concluded then in case of impossibility of its application, the substantive competence of the international court is concluded. The substantive competence of international court in terms of its subject, application, limits and powers is provoking more disputes. Albeit less acute with regard to its substantive competence. That is why there are those who believe that the jurisdiction of the Court is an infringement of the sovereignty of the state. The study aims to emphasize that the International Criminal Court is a complementary instrument to the national jurisdiction and not a substitute for national justice. Thus it does not infringe the sovereignty of state. this study uses the inductive approach to extrapolate the most important legal articles in the Rome Statute of the International Criminal Court and then analyze them in order to achieve satisfactory results of the possibility of adding new crimes to the substantive jurisdiction of the court and that its jurisdiction is not a substitute for national courts, therefore, there is no justification for refraining from signing and acceding to the Statute of the Court especially that the approval of the countries to the Rome Statute is an opportunity of getting benefit from joining to that court and the possibility of implementing and amending the Rome Statute in accordance with the legitimate interests of States.
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