They say they will continue the fight even though he has now left the US.
His deportation and trial comes after a German judge in Munich issued an arrest warrant in March, accusing Demjanjuk of assisting in the deaths of thousands of Jews at the Sobibor extermination camp in Nazi-occupied Poland.
Last month, an attempt to deport Demjanjuk was aborted after a court intervened following a petition from his family that he was too ill to be moved.
But that was overturned after US government investigators presented the courts with a recent video purporting to show Demjanjuk walking unaided.
On Monday, he was taken by ambulance from his home and put on board a chartered jet leaving Cleveland airport, Ohio, for Munich.
An airport official said Demjanjuk, using a wheelchair, said nothing as he was put on the aeroplane.
|Demjanjuk has twice been stripped of
his US citizenship [AFP]
Demjanjuk has been No 1 on a list of "Most Wanted Nazi War Criminals" compiled by the Los Angeles-based Simon Wiesenthal Centre – a body established to locate and bring former Nazis to justice.
Rabbi Marvin Hier, a founder of the centre, said Demjanjuk's case is expected to be the last trial of someone accused of Nazi war crimes.
"His work at the Sobibor death camp was to push men, women and children into the gas chamber," Hier said in a statement.
"He had no mercy, no pity and no remorse for the families whose lives he was destroying."
Demjanjuk's deportation is the latest and perhaps final chapter in a long series of legal moves against him.
|Prosecutors say they have evidence linking Demjanjuk to Nazi war crimes [EPA]
After moving to the US in 1952, he was stripped of his citizenship in 1981 when the US justice department ruled that he had hidden his past at the Treblinka concentration camp.
He was extradited to Israel in 1986 and sentenced to death two years later after a court found him guilty of war crimes and crimes against humanity.
In 1993 that verdict was overturned when Israel's supreme court ruled he was not the guard known as "Ivan the Terrible". His US citizenship was restored.
In 2002, his citizenship was again revoked following a civil complaint from the US justice department claiming he had worked at three other camps and had concealed that information when he first entered the US.
He was ordered deported in December 2006, but remained in the US fighting legal challenges and with no demands from other countries that he be sent to them.
Last year, Kurt Schrimm, Germany's chief Nazi war crimes investigator, asked prosecutors to charge him with involvement in the murder of 29,000 Jews.
Schrimm said he had evidence that Demjanjuk had been a guard at Sobibor and personally led Jews to the gas chambers.
Demjanjuk's son, John Demjanjuk Jr, told Reuters: "Given the history of this case and not a shred of evidence that he ever hurt one person let alone murdered anyone anywhere, this is inhuman.
"This is a vendetta in the falsified name of justice with the hope that somehow
Germany will atone for its past."