The defendants include a former Serbian president, Milan Milutinovic.
They are accused of joining former Yugoslav President Slobodan Milosevic in a "joint criminal enterprise" in 1998 and 1999 that included hundreds of murders and the forced expulsion of some 800,000 ethnic Albanian civilians from Kosovo.
The Serb crackdown led to the 1999 NATO air campaign that forced Serbian troops to withdraw from Kosovo.
The six have pleaded not guilty to the charges.
Milosevic died last March, bringing an inconclusive end to his trial for alleged war crimes.
(compiled from agency reports)