In October 1985, a group of Palestinians hijacked an Italian passenger ship, the Achille Lauro, held the passengers and crew hostage for several days, and murdered one of the passengers who was an American. The hijackers and the alleged mastermind of the hijacking were escaping in an Egyptian aircraft when they were intercepted by American military planes and forced to land in Italy. Italy took the hostagetakers into custody and eventually prosecuted and convicted them. However, Italy refused the request of the United States to arrest the mastermind of the hijacking operation and to hold him pending a formal extradition request. The mastermind was not detained in Italy and went to Yugoslavia. The government of Yugoslavia also refused the request of the United States to hold the mastermind pending an extradition request. The author examines the actions of Egypt, the United States, Italy, and Yugoslavia in the Achille Lauro case. He points out that the case raises important international law issues. One issue concerns the involvement of nation-states in international terrorism -- either before or after the terrorist incident. Another issue concerns the role nation-states play in the implementation and application of international criminal law. The author points out that Italy was obliged under the 1979 Hostages Convention to initiate prosecution or to extradite individuals alleged to have committed the crime of hostagetaking. Other issues discussed include Italy's release of the alleged mastermind, claims of diplomatic or other immunity by those breaking international law, double jeopardy claims under international law, the political offense exception under the Hostage Convention, prosecution for political crimes, and the nature of jurisdiction. 75 footnotes.