FACTBOX-What's at stake between U.S. and South Korea

(Reuters) - U.S. President George W. Bush visits South Korea on Tuesday for a summit meeting with President Lee Myung-bak, and will push to rid the Korean peninsula of nuclear weapons while sidestepping several other complicated fights.

Following are some issues between the political allies and trading partners that in recent years had to work through some tense disputes.

BEEF - Lee pushed hard and fast to strike a deal to reopen South Korea's market to U.S. beef in time for his first meeting as president with Bush in April, only to see it backfire at home and trigger massive protests on concerns that he was putting the public at risk of mad cow disease.

More than two months of protests have subsided but distrust of U.S. beef lingers in what was once America's third largest overseas market before a five-year ban.

TRADE - The two countries reached a free-trade deal in April 2007 but neither legislatures have ratified what would be the largest U.S. trade deal since the North America Free Trade Agreement 16 years ago.

The deal could boost the $80 billion (40 billion pounds) annual two-way trade between the United States and South Korea, its seventh largest trading partner, by as much as $20 billion, some estimates say.

NORTH KOREA - The two countries are involved in six-party talks aimed at ending North Korea's nuclear weapons programme in return for aid and better diplomatic standing for the communist state.

Washington has been pushing for tough inspection of the North's nuclear programmes after its recent declaration in return for a pledge to get it off the U.S. list of state sponsors.

MILITARY ALLIANCE - The military alliance between South Korea and the United States has evolved since U.S. troops fought against Northern forces in the 1950-53 war. The number of U.S. troops stationed in South Korea continues to fall and stands at about 28,000 and Washington has been pushing for Seoul to take on a greater share of paying for hosting them.