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In the ethnical conflicts in Rwanda in 1994, hundreds of thousands were massacred. UN Security Council, similar to the Former Yugoslavia genocide case, established an ad hoc tribunal by adopting Resolution No. 955 on 8 November 1994 under Chapter VII of the UN Charter. The main concern of this tribunal has been the prosecution of persons responsible for genocide and other serious violations of international humanitarian law. This paper, in a general view, examines the structure, competences, and the procedure of the Tribunal. Furthermore, specific aspects of the tribunal which are important from viewpoint of international law are examined. They include the legal base of the tribunal, the privileges and immunities of the tribunal, obligations of the states to cooperate with the tribunal, and the criminal justice in regard with witnesses, victims, accused and convicted. The article also, to some extent, will provide a comparative study between this tribunal and the International Tribunal for the Former Yugoslavia