Ex-Serbian President Milan Milutinovic is one of those charged
The men, including ex-President Milan Milutinovic, are charged with alleged war crimes committed by Serb troops during the conflict in Kosovo in 1999.
They deny murdering, persecuting and deporting ethnic Albanians.
The case comes four months after ex-Yugoslav President Slobodan Milosevic died in his cell during a trial on similar charges.
The BBC's Geraldine Coughlan in The Hague says that because the Milosevic trial was not concluded, this case is central to establishing legally what happened in Kosovo in 1999.
The six men are accused of forming a joint criminal enterprise with Mr Milosevic.
Mr Milutinovic will be in the dock alongside former Yugoslav deputy prime minister, Nikola Sainovic, ex-army chief of staff Dragoljub Ojdanic and three others.
They are charged with involvement in the murder, sexual assault and forced deportation of Kosovo Albanian civilians, as well as the destruction of their religious sites.
The indictment alleges that the accused aimed, among other things, to change the ethnic balance in Kosovo to ensure continued Serb control over the province.
The proceedings at The Hague may be lengthy.
The prosecution says it needs at last a year to submit its evidence and the defence is likely to take at least as long. BBC