They are the remnants of the group known as the 'Nauru 19', who were charged over an anti-government protest four and a half years ago.
Last year, they were granted a permanent stay on the charges when an Australian judge said they could never get a fair trial given the government's interference in the judicial process.
That stay was overturned, however, and another judge, Fiji's Daniel Fatiaki, was appointed.
The trial in the Supreme Court was controversial because the accused were denied legal representation.
All 15 people convicted have been remanded in custody while the court decides on their sentences.