The number of events that have been observed in the implementation of the Justice and Peace Law shows the relevance of this paper. Some of these events are summarized as follows: Confessions of multiple homicides stark outside the conflict, conceal ment of information relevant to the clarification of disappearances, torture and displacement of civilians, the persistence in the commission of crimes within the jurisdiction of the International Criminal Court and other related offenses. This set of facts can indicate that the Colombian state does not has the ability to judge the crimes committed in its territory, or is not interested in advancing prosecution, in either of both cases the state will be giving privilege to impunity, and therefore be leading to compliance with the requirements for the International Criminal Court to exercise its complementary jurisdiction.