The suits are in retaliation to the move last month by Creative, known for its Nomad and Zen products, in which it filed patent complaints against Apple in a federal court and with a US trade agency.
Creative also sought an exclusion order and a cease-and-desist order that would prohibit Apple from selling, marketing or importing its iPod players into the US.
Apple's new suit, filed in a Texas district court, claims that Creative has infringed at least three of its patents.
These are 'displaying data on a computer', the 'creation of icons to organise files on a computer', and 'editing data using a portable media device'.
Apple is asking for cash damages and a court order to prevent Creative from infringing on any other patents.
Apple's first countersuit alleged that Creative had infringed four of its patents.
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