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The court has dismissed claims of prejudice made against judges by two of the accused. They include the main defendant, Beate Zschaepe, who is charged with being a founding member of the cell, the National Socialist Underground (NSU).
Zschaepe, 38, is also charged with complicity in 10 murders, 15 robberies, two bombings and arson.
Prosecutors claim she torched the apartment in the eastern German town of Zwickau, where she lived with the NSU's two other alleged members, Uwe Mundlos and Uwe Boehnhardt.
Mundlos and Boehnhardt died in an apparent murder-suicide as police closed in on them after a robbery in November 2011.
Zschaepe, a trained gardener, faces life in prison if convicted. Her four co-accused in the trial face lesser charges of having assisted the NSU.
The case, the biggest in Germany to center on far-right extremism since World War II, is also expected to cast the spotlight on a botched police investigation into the NSU activities.
This includes the murders of nine immigrants and a German police woman that took place over a period of seven years, to 2007.
The trial will resume under tight security, with about 350 police deployed for Tuesday's hearing.
Prosecutors have called more than 600 witnesses in the trial, which observers say could run for more than two years.
Among those expected to provide evidence are relatives of the three alleged NSU members, as well as the group's former cohorts from the radical-right scene.
About 80 relatives of the NSU's victims are represented by around 60 lawyers at the trial.