Limiting nuclear proliferation is a vital goal of U.S. security policy. With this in mind, the Strategic Studies Institute cosponsored a conference at the University of Pittsburgh on March 16-17, 1994 to deal with the issues involved in achieving this objective. An additional U.S. objective is the stabilization of relationships among the members of the Commonwealth of Independent States. These two issues come together in Ukraine which, upon achieving independence, found itself in possession of nuclear missiles that were positioned in the former Soviet Union and on Ukraine's territory. Ukraine was reluctant to relinquish control of them for security reasons. This monograph, presented at the conference, seeks to explain why Ukraine originally sought to retain the weapons and then, in 1994, agreed to dismantle them in return for compensation and the very limited security guarantees that exist under the 1968 Non-Proliferation Treaty. The author also examines the nature of Russia's threat to Ukraine and the implications of the new agreement for U.S. policy vis-à-vis Ukraine and Russia.