The adoption, on the 17th July 1998 at Rome, of the International Criminal Court’s Statute (ICC Statute), was a consequence of the crimes against humanity committed beginning with the Second World War. The ratification of the present Statue by the states have raised a series the problems related to the surrender of own citizens, to the parliamentary immunity and the immunity of the head of state, etc. The most important problem referred to the attempt of states to exempt its own citizens from the jurisdiction of the ICC. The most interesting case is that of the USA, which launched an active campaign in order to sign, based on art 98 of the ICC Statute, agreements on non-extradition of its own citizens with the states that signed the ICC Statute. The advantages and disadvantages of signing such an agreement depend directly on the foreign policy of a state towards NATO and EU.