Dionyssis Liakopoulos, 25, and Christos Steriopoulos, 29, risk a life sentence if found guilty of the drive-by killing of Shehzad Luqman in Athens in January.
They were arrested a few hours after the murder when a taxi driver who witnessed the attack reported their motorbike numberplate to police.
According to the driver, the pair drove up behind the victim and assaulted him as he cycled in the Petralona neighbourhood near the Acropolis.
A search of Liakopoulos' home uncovered leaflets from the neo-Nazi party Golden Dawn, according to Kostas Papadakis, one of the plaintiff's lawyers.
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Steriopoulos, for his part, said in a written statement he was "saddened" by Luqman's "tragic death" and claims he only hit him in the leg.
Both accused deny being members of the neo-Nazi party and Steriopoulos has rejected "any ideological involvement in Golden Dawn" and allegedly condemns the party.
Both men say they got into an argument with the victim after he blocked their path with his bicycle.
But Petros Konstandinou, of an anti-fascist movement, rejected their statements, telling the press, "In cases like this, they always deny".
Pakistani community representative Ashlam Tzavent claimed Golden Dawn was responsible for "six or seven murders" and "dozens of attacks" that have never been prosecuted.
Human rights and immigrant defence groups have called a rally for later today outside the Athens courtroom, where the trial opened under a heavy police presence.
Hearings were suspended shortly after the trial opened to settle procedural matters, including to allow time for the victims' parents to arrive after their plane from Lahore was delayed.
In the morning, about two dozen human rights and immigrant defence activists protested outside the courthouse. Steriopoulos's parents were verbally harassed during a break.