The suit contends that Apple was fully aware of problems with the " defectively designed" Nano before it was launched but decided to go ahead anyway.
Users have complained that the screens crack very easily and are very poor at resisting scratches.
"Although [the] defendant knew that there were problems in the design of the Nano, the defendant did not recall the defectively designed Nanos waiting for sale to other consumers," said the filing in the US District Court in San José, California.
"Instead the defendant permitted class members to purchase the defectively designed Nanos and pass the expense, hassle and frustration of replacing the defectively designed Nanos along to class members."
The suit asks for compensation, punitive damages, all legal costs and part of the profits from Nano sales.
The suit was launched by Jason Tomczak, who claimed that he would not have bought one of the media players had he known about the defects.
In the filing Tomczak points out that advertising for the Nano featured Apple chief executive Steve Jobs carrying the media player in his pocket.
But the filing states that even carrying the Nano in the same pocket as the earphones quickly renders the screen so scratched that it becomes unusable.
Apple has acknowledged problems with the Nano, claiming that "less than one-tenth of one per cent" of stock was fitted with screens that were too weak and prone to cracking.
But it has denied that the screens scratch easily, saying that they are made of exactly the same material as the iPod Mini, which the Nano replaces.
The suit counters by saying that, while the screen may be the same material, there is a protective layer of resin on top to protect against scratches. This was much thinner in the Nano than with previous models, which explains why the screen scratches so easily.
An article in the Wall Street Journal Online seemed to confirm elements of the problem, with the Nano reviewer saying that no other media player had ever become so scratched so quickly.
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