The International Criminal Tribunal for Rwanda (ICTR) was created by the Resolution 955 of 8 November 1994. This tribunal was established for prosecution of persons responsible for genocide and other serious violations of international humanitarian law committed in the territory of Rwanda, and Rwandan citizens responsible for such violations of international law committed in the territory of neighbouring States, between 1stJanuary and 31st December 1994. This article analyzes the trial rendered by the ICTR for defendants who were prosecuted for the crime of conspiracy to commit genocide for acts committed in the years prior to 1994. The case of Colonel Théoneste Bagosora, Ferdinand Nahimana and their co-defendants have served us as examples to examine whether or not the period of the temporal jurisdiction of ICTR had an impact on the establishment of evidence presented by the Prosecutor. In these trials, the prosecutor was criticized by the judges for presenting the evidences of crimes that were committed outside the temporal jurisdiction, thus, the accused of the crime of conspiracy to commit genocide were acquitted.