The men are accused of aiding the abduction and murder of two bankers in Kazakhstan in 2007.
The main suspect, Rakhat Aliyev, was found hanged in his prison cell in Vienna in February. His lawyers believe his death was not a suicide and further tests are expected into apparent traces of a sedative in his body.
More than 60 witnesses, mostly from Kazakhstan, are set to testify at Vienna regional court, some via video link. The security presence inside the courtroom is expected to be substantial.
The charges relate to the killing in 2007 of two managers of the Kazakh Nurbank, in which Aliyev was a major shareholder.
His associates Alnur Mussayev, a former head of the Kazakh intelligence service, and Vadim Koshlyak, a former presidential bodyguard, are now at the centre of the trial.
Vienna prosecutors allege that they helped Aliyev to hold the two managers against their will and forced them under threat to hand over shares and property rights.
The two bankers' bodies were not found until May 2011, buried in lime-filled barrels on waste ground in Almaty. They had had plastic bags put on their heads and were strangled.
Aliyev, a former ambassador to Austria, always maintained that the murder charges were politically motivated and trumped up by rivals in his homeland. He was the former son-in-law of Kazakhstan’s authoritarian president, Nursultan Nazarbayev.
The pair fell out in 2007, and Aliyev was sacked from his post as ambassador in Vienna and sentenced in absentia to 40 years in prison for organised crime and an attempted coup.
Austrian authorities refused two extradition requests by Kazakhstan and began their own investigations, issuing an arrest warrant last May.
Aliyev (52) handed himself in and spent eight months in investigative custody until he was found dead in his cell on 24 February.
On the day of his death he had been due to testify against other inmates who he said had blackmailed and threatened to kill him while making it look like suicide.
Austrian authorities say video footage and electronic door control systems showed no unauthorized people had entered Aliyev's solitary confinement cell before his death.