...from the DOJ's website:
9-15.100 - General Principles Related to Obtaining Fugitives from Abroad
International extradition is the formal process by which a person found in one country is surrendered to another country for trial or punishment. The process is regulated by treaty and conducted between the Federal Government of the United States and the government of a foreign country. It differs considerably from interstate rendition, commonly referred to as interstate extradition, mandated by the Constitution, Art. 4, Sec. 2.
Generally under U. S. law (18 U.S.C. § 3184), extradition may be granted only pursuant to a treaty. However, some countries grant extradition without a treaty, and of those that do, most require an offer of reciprocity. Further, 18 U.S.C. 3181 and 3184 permit the United States to extradite, without regard to the existence of a treaty, persons (other than citizens, nationals or permanent residents of the United States), who have committed crimes of violence against nationals of the United States in foreign countries.
www.justice.gov
..and Dept of State (archived) as of 2001:
VENEZUELA
The current extradition treaty between the United States and Venezuela was signed in 1922. The treaty contains a limited list of extraditable offenses,
and narcotics trafficking is not one of the listed offenses. Venezuela is a party to the 1988 UN Drug Convention, and by the terms of the Convention narcotics trafficking and related money laundering are deemed extraditable under the bilateral extradition treaty. Venezuela's 1999 Constitution expressly prohibits the extradition of Venezuelan nationals. Previously, Venezuela had only a statutory bar to the extradition of nationals. Despite this obstacle, Venezuela has demonstrated good faith in extraditing non-Venezuelans to the United States. Since the last report, Venezuela has extradited one non-national to the United States.