Divided into four major parts, this document explains the significance of the Liberal Democratic Party (LDP) in Japan. Part 1 indicates that the LDP has governed Japan since 1955 and controls 445 seats in the 764 seat parliament. The selection of the prime minister, chosen from within the ruling party, is seen as vital to U.S. interests. For example U.S.-Japanese trade totaled 109 billion dollars in 1986. The last prime minister, Yasuhiro Nakasone, presided over major changes in both politics and Japanese society. The primary concern for the United States is whether the new prime minister can reduce the current tension in U.S.--Japanese relations. Part 2 of the report describes the selection process for the prime ministers by the party members. Part 3 provides profiles of the four candidates and describes the legacy of Nakasone. Part 4 outlines the key issues and implications of the election for the United States. The new prime minister will face several key tasks that include restructuring the economy, stabilizing the yen, and maintaining a base of support. Party support comes from farmers and rural residents, and the electoral process is candidate centered rather than party centered. LDP is the most conservative party but is perceived as flexible and responsive to public pressure. Party power is limited, and the bureaucracy plays a greater role in drafting legislation than in the United States. Appended are an economic fact sheet, a genealogy chart of LPD's five major factions from 1965-87, and a list of Japan's prime ministers from 1946-1987. (NL)