'Last Nazi trial'
Demjanjuk, 89, is accused of being an accessory to the murder of 27,900 Jews at the Sobibor camp in occupied Poland from March to September 1943.
The case, likely to be the last major Nazi trial, is the first time that a non-German has been tried in Germany over the Holocaust, in which an estimated six million Jews were killed.
He could face up to 15 years in prison if convicted.
"When the bell tolls for John Demjanjuk, it is also tolling for every other war criminal"
Rabbi Marvin Hier
Harry Smith, Al Jazeera's correspondent in Munich, said Demjanjuk's lawyer argued that the court had no jurisdiction "because the accused was Ukrainian [and] the alleged offences took place in Poland, albeit German-occupied Poland.
"However the authorities here argue that many of the alleged victims were German-Jew. They say that Demjanjuk spent some time after the war in a displaced persons camp near Munich, so they have the jurisdiction and they have every intention of prosecuting this case. "
Smith said that it was difficult to tell whether Demjanjuk, who appeared to have his eyes closed, was following proceedings closely.
Despite concerns over his health, the defendant has been declared fit to stand trial, although proceedings have been limited to 90-minute sessions a day.
A doctor who examined Demjanjuk two hours before the trial began said his vital signs were all stable.
Efraim Zuroff, a Nazi-hunter at the Simon Wiesenthal Centre, said it was important that the trial was taking place, but felt that Demjanjuk may have been trying to look more ill than he was.
"He has a vested interest in appearing as sick and as frail as possible. And he's going to play it up to the hilt," Zuroff said.
Demjanjuk says he fought in the Red Army before being captured by the Germans in 1942, and said that although he was recruited as a camp guard, he was not placed at Sobibor.
But Israeli and US courts have established he was at the camp, where prosecutors say Jews were killed with a toxic mix of carbon monoxide and carbon dioxide.
Jewish groups and victims' families say that the case is symbolic.
"We should not make the mistake of thinking that a case against one war criminal is a case against just one man," Rabbi Marvin Hier, Dean of the Wiesenthal Center in Los Angeles, said.
"When the bell tolls for John Demjanjuk, it is also tolling for every other war criminal. Even if it just gives them sleepless nights," he told the Reuters news agency.
Demjanjuk was sentenced to death in Israel in 1988 for being "Ivan the Terrible" - a particularly sadistic Nazi guard, but after five years on death row it emerged the court had convicted the wrong man.
The Ukranian emigrated to the US in 1951, becoming a naturalised citizen seven years later, and worked in the auto industry. He was extradited in May this year.