Greece began hearing the asylum claim Friday of the first of eight Turkish military officers who fled their country after the failed coup on July 15, the asylum service said.
Captain Feridun Coban was driven to the headquarters of the asylum service in Athens in the early hours of Friday morning, according to the group's lawyer Stavroula Tomara.
His fellow officers - three other captains, two commanders and two sergeants, who along with Coban are accused by Turkey of involvement in the coup - will have their cases heard from Monday.
No decision will be made in their cases for "two or three months", according to the asylum service.
Greece said Thursday that Turkey had formally requested the extradition of the men on suspicion of involvement in the failed coup. The men deny the accusations.
The asylum service said the cases will "follow a totally normal procedure" despite pressure from Ankara to hand the men over, with the issue threatening to strain ties between the uneasy NATO allies.
The men requested asylum in Greece after landing a military helicopter in the northern city of Alexandroupoli, four days after the attempted government takeover on July 15.
In late July, the court of Alexandroupoli sentenced the eight -- who face a military trial in their homeland if sent back -- to suspended two-month prison terms for illegal entry.
The eight claim they will not receive a fair trial in Turkey, where the authorities have detained tens of thousands of people over the coup, including top generals.
If sent home, their lives could be in danger, one of their lawyers has claimed.
Tomara said that if they were extradited there would be risks "for their security and their lives, as well as those of their families."
Greece and Turkey's prime ministers spoke by phone Thursday to discuss "matters of judicial cooperation," Athens said.
Ties between Greece and Turkey have improved in recent years as the two countries have pursued a policy of normalisation but have been strained by territorial disputes over the Aegean Sea and the status of Cyprus.
Athens has also been dependent on Turkey to help it control the wave of migrants who have arrived on its shores since 2015 heading towards northern Europe.