A Tweet sent to everyone trying to log onto one Nazi website said: 'We wish all Nazis a good start to the New Year.'
They have been joined by hackers in Spain, who posted a list of 1,000 alleged customers from a far-right shop.
Anonymous's leaks site is called 'NaziLeaks'.
Information on the operation - dubbed Operation Blitzkrieg - is circulating on Twitter tagged 'OpBlitzkrieg' and 'NaziLeaks'.
At present the Nazi-Leaks website says that its account has been suspended.
As usual with Anonymous's more public attacks, such as their Operation Darknet attack on paedophiles, information has been 'mirrored' on other sites to make it harder for 'victims' to get rid of. Read More