This article examines the distinctive legal nature of mixed (hybrid) tribunals and the implications of their institutional design for international cooperation and judicial assistance. The study concludes that the agreements signed with the United Nations establishing these judicial bodies impose obligations of cooperation only upon the States parties to the relevant agreements and do not give rise to a corresponding general obligation on the third States. The examples of the Special Tribunal for Lebanon demonstrate that the absence of a binding obligation requiring third States to cooperate with mixed (hybrid) tribunals may materially constrain the effectiveness of their judicial activities. At the same time, political support from the United Nations Security Council may, under certain circumstances, mitigate, at least in part, the structural weaknesses of the applicable regime of international cooperation and judicial assistance.