The pair were taking part in a dancing competition in Bavaria a few weeks ago and didn't realise they were being filmed.
The incredible clip has been shared 1.6 million times, with more than 44,000 comments.
Dietmar said: 'We are quite flabbergasted what the video has set in motion.
'I had not even seen anyone filming us!'
A video shows the pair, originally born in Austria, dancing to Down the Road Apiece by The Refreshments.
They can be seen twisting and twirling on the dance floor as the audience cheers them on.
The pair were awarded the veterans cup for their incredible routine.
The couple have won several amateur competitions in the Boogie Woogie category.
They have won the Austrian Championship four times, as well as the German Championship.
They even give courses and workshops to pass on their skills to the next generation.
Nellia said: 'We simply enjoy the music and wanted to see old friends again.
'This dance has become an integral part of our lives. We discovered the 1950s music scene and found like-minded people at concerts and festivals.'
The couple say they never expected to become an online video sensation.
But a younger generation of netizens adore their dance moves.
One netizen, called Cynthia Seabra wrote: 'You are never too old to rock it if your health is good and your spirit stays forever young.
'Well done to the both of you.'
/Daily mail/
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