Mexico’s signature of the Rome Statute of the International Criminal Court, derive implicit and explicit commitments that must be met. On the one hand, the obligation to define, in the domestic sphere, crimes jurisdiction of the Court and, on the other, the obligation to have in place provisions penalizing offenses against the administration of justice in procedures performed at court or in connection with it and also allow secure procedures applicable to all forms of cooperation envisaged in the Statute. This paper explores the various ways in which States have sought to fulfill these obligations and proposes ways that would be more feasible in the case of Mexico, with particular reference to the crime of genocide, crimes against humanity and war crimes.