"Defendant's entire business amounts to nothing more than a massive infringement of plaintiffs' exclusive rights under the Copyright Act and New York law," says the law suit.
Arista, Warner Brothers, Capitol and Universal are amongst the major companies behind the suit. It claims that Allofmp3.com profits by selling music which they own the rights to without their permission and without compensation.
When an online retailer sells music it typically pays royalties to artists via a collecting society such as the Performing Rights Society (PRS) or the Mechanical Copyright Protection Society (MCPS).
Allofmp3.com says that it follows Russian copyright law and that it pays royalties to a Russian collecting society, the Russian Multimedia and Internet Society (ROMS). Record industry body the International Federation of Phonographic Industries (IFPI) says that the collecting society does not pay artists or record labels any of those royalties.
ROMS itself says that the site is legal because it licenses it. "Allofmp3.com's activity is quite legitimate," ROMS general director Oleg Nezus told BBC Russia earlier this year. "The opinion of foreign copyright owners is just that - their opinion."
The website sells mp3s of popular music at a steep discount to normal prices. An album which would cost around £6 on iTunes costs just 60p on Allofmp3.com, and the site is the second biggest paid download destination for UK users, behind Apple's iTunes.
The lawsuit is being pursued against Mediaservices, the company behind Allofmp3.com. It seeks a court order against the company and also punitive and compensatory damages. UK music body the BPI is already suing Mediaservices in the English courts.
Earlier this year credit card companies Visa and Mastercard stopped processing payments to the site because of the alleged infringements.