Police arrested the pair separately in the central German towns of Marburg and Baligen last Tuesday, Der Spiegel reports.
The woman was apparently listening to encrypted radio messages at the time, police told the magazine.
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Known only as Andreas A. and Heidrun A., the suspects are accused of spying on behalf of the Russian Foreign Intelligence Service, SVR.
They are believed to have been active in Germany since before the country's reunification, in the era of Russia's KGB intelligence agency.
Both of them deny the charges.
A search of their residence found two Austrian passports that police say are forged. The passports identify Andreas A. as an Argentinian national and Heidrun A. as Peruvian, yet German authorities in South America have confirmed that this information is false.
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It is not known what the alleged spies' target was, Der Spiegel says.
Police began investigating the couple after a Russian spy ring was uncovered in the United States last year, according to The Local.
It is the first time undercover foreign agents have been found in Germany since the county was reunified in 1990.
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