It said the three accused, aged 88, 92 and 94 years old, are believed to have been involved in the murder of prisoners at Auschwitz in Nazi-occupied Poland.
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They were arrested after police searched six homes in the state of Baden-Wuerttemberg using information released to several German states last autumn by the Central Office of the Judicial Authorities for the Investigation of National Socialist Crimes.
Various documents from the Nazi era were seized during the search on Wednesday and are being evaluated, prosecutors said.
Some 1.5 million people perished at Auschwitz, mostly Jews but also Roma, Poles and others, between 1940 and 1945.
German officials are trying to track down other low-level collaborators in a "last chance" hunt for ageing perpetrators of the Holocaust, in which some 6 million Jews were murdered.