Whoever wins the race for the leadership of Japan's ruling party, the Liberal Democratic Party (LDP), is also likely to become prime minister, as a LDP-led coalition holds the majority in Japan's Lower House of parliament.
Essentially, the battle for leadership is a fight between the rival factions in the LDP.
HOW THE VOTE WORKS
657 votes: 357 from LDP MPs and 300 from LDP rank and file
A candidate getting more than half wins
If no-one gets more than half, just the LDP MPs vote again
Incumbent leader Junichiro Koizumi has the support of two powerful faction leaders - former Prime Minister Yoshiro Mori and LDP General Secretary Taku Yamasaki.
The biggest LDP faction - that led by another former Prime Minister, Ryutaro Hashimoto - is split between pro-Koizumi and other supporters.
Junichiro Koizumi, 61, incumbent leader
Junichiro Koizumi has called for less public spending and a grip on banks' bad loans. His re-election campaign is focused on creating more jobs, and fighting both deflation and debt.
He is pushing for a close relationship with the US and he favours revising Japan's pacifist constitution.
Although his handling of the economy has been disappointing, he remains popular with the public.
Shizuka Kamei, 66, former LDP policy chief
Shizuka Kamei is a long-term enemy of Junichiro Koizumi. He was beaten to LDP leadership by Mr Koizumi last time, in April 2001.
He favours more public spending to reinvigorate the economy, and wants a more distant relationship with Washington.
A former policeman, Mr Kamei has also called for the abolition of Japan's death penalty - unusual within the LDP
Masahiko Komura, 61, former foreign minister
Masahiko Komura also favours more public spending, but acknowledges that it can be wasteful and wants checks to ensure future works make economic sense.
He wants Japan to become a permanent member of the UN Security Council in the next five years.
Takao Fujii, 60, former transport minister
Takao Fujii too wants greater public spending - 10 trillion yen of it - but wants it to be more focused.
He also advocates more help for small and medium-sized companies.