The men, aged 18, 19 and 26, arrived in Germany at the end of 2015, at the height of the influx of migrants. They were arrested at homes for asylum-seekers in September.
All three are charged with membership in a terrorist organization. Two of them also are charged with using forged documents, and the third with attempting to do so.
Defendants don’t enter formal pleas in Germany. News agency dpa reported that they declined to address the allegations against them as the trial opened Tuesday at the Hamburg state court.
The trial is scheduled to continue until early November.