Russian state news agency TASS cited a source in the power structures of the self-proclaimed Donetsk People’s Republic (DPR) as saying criminal cases had been opened and charges filed against Dylan Healy, 22, and Andrew Hill, 35.
It said both men were refusing to cooperate with the court in the territory which is only recognised by governments in Russia and Syria.
On April 29, Russia’s defence ministry released a video showing an injured British man captured in Ukraine, who said his name was Andrew Hill being questioned by unidentified Russian forces.
They said he had surrendered to Russian troops in southwestern Ukraine and had been carrying a weapon.
Mr Healy is reported to be a humanitarian volunteer believed to have been detained at a checkpoint in southern Ukraine.
Last month, two Britons and a Moroccan were sentenced to death for “mercenary activities” after being captured fighting for Ukraine against Russia and Russian-backed forces, in what Western politicians decried as a show trial.
Their relatives say they were contracted to fight for the Ukrainian army, and therefore were not mercenaries but regular soldiers entitled to the protection of the Geneva Conventions on treatment of prisoners of war.
TASS reported on Friday the DPR Supreme Court had received appeals from lawyers for Brahim Saadoun and Shaun Pinner, but that the other Briton, Aiden Aslin, had yet to submit an appeal.
TASS cited the court as saying the appeals would be considered within no more than two months.
It said Pinner had asked for his sentence to be commuted to life imprisonment.
Britain has declined to deal publicly with Russian proxy authorities in the DPR that it does not recognise, preferring to ask Kyiv for assistance. Russia has said the men’s fate is a matter for the DPR.