This thesis aimed at studying the roles played by the international community in the prevention and punishment of the crime of genocide under international law. In other words the research work deals with the roles of the international criminal tribunal/ courts in the prevention and punishment of the crime of genocide under international law. The justification of this research work arose out of the need to confront Genocidal crimes of recent times and also the ones committed in the past for deterrence purposes through investigation, prosecution and punishing of those responsible for such crimes. However in the course of this research a major finding (among others) is that the provisions of the Convention are far from being adequate to cure the challenges that arose in international practice posed to the Convention, in the course of the implementation of the convention coupled with fact that there is no clear, direct and effective judicial response to the prevention and punishment of the crime of Genocide, because there is no nexus between the Convention and the State parties in combating the crime of Genocide. This finding clearly constituted a major problem of this research work. In this regard therefore the objective is to identify the reasons accounting for the poor implementation of the Genocide Convention in practice vis a vis the adequacy or otherwise of the provisions of the convention in international law. Thus, in view of these events this research is concluded by recommending that in order to put an end to impunity for the perpetrators of these crimes and also in an attempt to prevent the crime of genocide there should be in place an effective legal mechanism to enforce implementation at all levels (i.e local and international). The sources of information relied upon for this research are relevant text materials, international instruments, Journals (both local and International), judicial authorities and internet materials.