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.

The study, by the Institute of Education, London University, examined the reading habits of 6,000 children.
It indicated reading for pleasure was more important to a child's development than how educated their parents were.
The researchers concluded a wide vocabulary helped children absorb information across the curriculum.
They analysed the results of tests taken at the age of 16 by 6,000 children, all born in one week, from the 1970 British Cohort Study.
The findings showed those who had read often at the age of 10 and had been reading books and newspapers more than once a week aged 16 had performed better than those who had read less.
There was a 14.4% advantage in vocabulary, a 9.9% advantage in maths and an 8.6% advantage in spelling, the research found, once parents' background and reading habits were taken into account.
The study said: "The influence of reading for pleasure was greater than that for having a parent with a degree."
The total effect on children's progress of reading often - reading newspapers at age 16 and being a regular library user - was four times greater than the advantage of having a university-educated parent, the study suggested.
The Institute of Education also looked at the impact on test scores of having brothers and sisters and found that those youngsters with older siblings were less likely to do well, particularly in vocabulary.
It suggests this could be because children in larger families spend less time talking one-to-one with their parents and have less chance to develop their vocabulary skills.
There was less effect if children had younger brothers and sisters, although they may score lower on vocabulary, the study found.
Study author Dr Alice Sullivan said: "It may seem surprising that reading for pleasure would help to improve children's maths scores.
"But it is likely that strong reading ability will enable children to absorb and understand new information and affect their attainment in all subjects."
Speaking on BBC Radio 4's Today programme, she said: "It absolutely makes sense that you would expect reading for pleasure to improve children's vocabularies.
"But I think that that also does improve children's ability to take on new information and new concepts across the curriculum.
"A child who has a narrow vocabulary may constantly be coming across things they don't understand."

The multiple TT winner set the fastest time of the week in the Classic event on his Yamaha Superbike at 125.49mph.
Anglesey's Barry Lee Evans topped the Senior MGP board while home rider Michael Evans moved to the top of the Junior leaderboard.
Michael Evans' 119.228mph lap was the fastest Manx Grand Prix time so far.
Darryl Field leads the Newcomers' section after a lap of 115.09mph.
The session was cut short as mist fell on the mountain section with qualifying to continue on Friday evening with the first racing on Saturday.
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.
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Children who read for pleasure are likely to do better in maths and English than those who rarely read in their free time, research suggests.
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New Zealand racer Bruce Anstey continued to set the pace in the fourth qualifying session at the Isle of Man Festival of Motorcycling.