The September 4th 2009 bombing by US planes near the northern Afghan city of Kunduz on two fuel tankers stolen by insurgents killed and wounded dozens, prompted outrage in Germany and a political scandal.
Seventy-nine families are seeking €3.3 million ($4.3 million) over the bombing which Germany's Bundestag lower house of parliament described as "one of the most serious incidents involving the German army since the Second World War."
The hearing in the western city of Bonn will initially focus on the claims by a father seeking €40,000 after the death of two of his children and a widowed mother-of-six whose claim amounts to €50,000.
Germany has said it would ask the court to reject the lawsuit, according to a statement by the court in Bonn, which is hosting the hearing because the Defence Ministry is still based in the former German capital.
Plaintiffs and witnesses have not been invited to Wednesday's hearing.
Karim Popal, the lawyer for the victims, says 137 civilians were killed in the strike but Germany has never confirmed the figure, which officially stands at more than 90 dead and wounded.
"Due to this barbaric crime, many orphans and widows have lost the person who fed them and many mothers have lost their children," Popal, a German-Afghan, said.
In response to a sharp rise in attacks on foreign forces, a German commander called in the raid, which forced the defence minister at the time to resign and claimed other high-ranking scalps.
Chancellor Angela Merkel had to appear at a parliamentary committee of inquiry.
Germany has already paid out around $430,000 to families affected by the Afghan air strike which, it underscored, was not compensation but humanitarian aid.
Berlin has around 4,400 troops in Afghanistan but is gradually reducing its numbers, more than a decade after the initial deployment, from an all-time high of 5,350.
The country is the third-largest contributor of troops to NATO's International Security Assistance Force (ISAF), behind the United States and Britain.
It has agreed with its NATO partners to gradually pull combat forces out of the country by the end of 2014 as Afghan troops assume more responsibility for security.
But it plans to maintain a military presence from 2015 assisting Afghan forces.