Former Yukos oil tycoon Mikhail Khodorkovsky has appealed against his conviction for fraud and tax evasion.
Supporters of Mr Khodorkovsky say he was subjected to a 'show' trial
Mr Khodorkovsky was sentenced to nine years in prison at the end of May and his lawyers have described the charges as "illegal and unfounded".
The charges against Mr Khodorkovsky, once one of Russia's richest men, have been seen as politically motivated.
Lawyers for associate Platon Lebedev are also appealing the verdict.
Both Mr Lebedev and Mr Khodorkovsky were found guilty on six out of seven counts of fraud and tax evasion on 31 May and sentenced to nine years in prison.
Mr Lebedev and Mr Khodorkovsky were also ordered to pay 17bn roubles (£330m; $600m) in taxes and penalties.
Mr Khodorkovsky has branded the charges against him as trumped up to "plunder" Yukos.
His supporters say Mr Putin's real gripe is that the former oligarch used his considerable wealth to influence political change.
US President George W Bush has expressed concerns about the trial to Moscow, suggesting to Western media that Mr Khodorkovsky was judged guilty before even standing trial.
Genrikh Padva, one of Mr Khodorkovsky's lawyers, said: "The defence thinks the verdict is illegal and unfounded and asks that it be cancelled and the trial halted."
Yelena Lipster, a lawyer for Mr Lebedev, told the Itar-Tass news agency that "we have lodged a complaint requesting to overturn the verdict by the Meshchansky court".
However, Russian president Vladimir Putin has always maintained he is simply trying to recoup the back taxes the state is owed by the oil company Mr Khodorkovsky used to run.
Yukos was forced to sell Yuganskneftegas, its main oil-producing arm, as part payment towards $27.5bn in back taxes the state said it owed.
Yugansk is now owned by Russian state firm Rosneft.
Russian prosecutors have threatened to bring additional charges against Mr Lebedev and Mr Khodorkovsky.