While crime -- assault, drug smuggling, theft, and arson -- has become a problem in Antarctica, it is doubtful whether a U.S. court could exert jurisdiction over a criminal case involving an American national or American property. The 1959 Antarctic Treaty did not affect previously asserted territorial claims. Although the civilian population has increased while the military presence has decreased, the Treaty only explicitly addresses personal jurisdiction with respect to certain classes of civilians such as observers conducting inspections under the Treaty and exchange scientists. These 'privileged nationals' are subject to exclusive jurisdiction of their own nations. In cases of conflicting jurisdiction involving nonprivileged nationals, the Treaty only says that concerned nations should consult with one another to reach an acceptable solution. While the United States clearly has jurisdiction over military personnel, its jurisdiction over support personnel and tourists is uncertain. The Supreme Court holds that civilians may not be subject to military courts in peacetime, no Federal criminal statutes specifically address the Antarctica area, and a literal application of 18 U.S.C. Section 7 on special and terrotorial jurisdiction could lead to anomalous situations. A 1977 bill proposed in Congress to address these problems received strong support, but was never passed. However, the Antarctica situation poses some constitutional problems for such a law relating to speedy trial and search and seizure. Under international law, the United States could exercise jurisdiction over its own nationals, but not foreign nationals. The applicability of traditional principles of jurisdiction to Antarctica mandates consideration of alternative solutions. One promising approach requires an examination of the offense itself, rather than the nationality of the offender or the victim. A determination of the applicable law, and therefore the applicable forum, would be made by applying the law of the country having the most contact with the crime. The paper includes 111 footnotes.