Friday, September 24, 1999 Published at 18:07 GMT 19:07 UK
China's key players
State President: Jiang Zemin
His choice was Jiang Zemin, at the time the Mayor of Shanghai, and a relatively unknown party functionary.
Deng lived for another eight years, a crucial time in which Jiang consolidated his power, in particular with key allies, now known as the "Shanghai faction" in the party, military and People's Armed Police.
In 1998, he became the first Chinese president to visit the US since the 1980s.
But Mr Jiang is facing slowing economic growth, and the political challenge of preparing a handover of at least some of his power to a younger leadership.
Further analysis: China's big party
Prime Minister: Zhu Rongji
The economic reformer fulfilled his mandate to overhaul crumbling state industry and rescued a banking system that was technically bankrupt.
Mr Zhu is popular with Chinese people because of his anti corruption drives, but has also proved himself adept at charming international audiences with his blunt, often self-deprecating style, and ready smile.
In 1989 as Mayor of Shanghai, he managed to avoid the bloodshed associated with demonstrations in the capital. As popular protests spread to Shanghai, his public pledge not to call in the army to disperse demonstrations was widely felt to have defused a major crisis in the city.
Although Mr Jiang and Mr Zhu have worked together for nearly 10 years, Mr Zhu has never been considered part of the president's inner circle.
Further analysis: The laughing prime minister
Head of NPC: Li Peng
In March 1998, he was elected head of China's de-facto legislative parliament - the National People's Congress, but with a large number of dissenting votes.
Cautious and uncharismatic, Mr Li is reviled both at home and abroad for introducing martial law during 1989's pro-democracy demonstrations in Tiananmen Square, which paved the way for the brutal military crackdown.
But his supporters are powerful, and Mr Li remains the highest ranking member of the Communist Party's all-powerful Politburo standing committee after President Jiang Zemin.
Further analysis: Li Peng remains China's No. 2
Vice-President: Hu Jintao
He is clearly trusted by Jiang Zemin and is widely expected to succeed him as general secretary if Mr Jiang steps down from his party job in 2002.
If this speculation is correct, he would be the first paramount leader of China whose party career began after the Communist takeover in 1949.
For much of the 1980s and early 1990s, Mr Hu served as party chief of the remote provinces of Tibet and Guizhou, where he demonstrated his toughness in the crackdown on separatist activity.
As vice-president Mr Hu comes into considerable contact with visiting heads of state and spends time touring abroad.