The "Freital Group", named after the suspects' hometown near Dresden, consists of seven men and a woman.
The German nationals are accused of targeting refugees and left-wing groups in 2015, causing two injuries.
The female suspect confessed to carrying out the attacks, while the men refused to speak in court.
The alleged members - aged between 19 and 39 - face life imprisonment if found guilty of attempted murder, and up to 10 years if the court rules they were part of a terrorist group.
Their names have not been publicly released.
"They wanted to create a climate of fear and repression," federal prosecutors said last year as they prepared the case.
"The aim of this group was to carry out bomb attacks on asylum-seeker shelters, as well as on the apartments, offices and vehicles of those with differing political views."
The group is accused of targeting refugee accommodation in Freital and a left-wing housing project in Dresden with explosive devices in 2015.
In one of the assaults, the suspects threw explosives through the windows of a home for refugees, the prosecutors say.
The suspects are also alleged to have targeted a left-wing councillor's car in Dresden.
The trial is being held amid tight security.
In 2016, there were about 3,500 attacks against refugees and asylum seekers across Germany, the AFP news agency reports citing data by the German interior ministry.
More than 560 people - including children - were injured during the assaults.
Eight suspected members of a far-right group in Germany have gone on trial in the eastern city of Dresden, charged with terrorism and attempted murder.