Apple filed its latest suit in a district court in Texas last Thursday, claiming Creative has infringed at least three of its patents -- one that involves displaying data on a computer, another for editing data using a portable media device, and the third for the creation of icons to organize files on a computer.
Apple is seeking cash damages and a court order to prevent further patent infringements.
Apple's first counter-suit, filed last month in the district court in Wisconsin, alleged Creative had infringed four of its patents.
Apple's second counter-suit was filed in a district court in Texarkana, Texas, which handles a disproportionate share of major patent cases in the United States.
Legal experts have found that patent trials put before juries in the court have favored patent holders, suggesting that Apple has chosen the venue as a means to put pressure on Creative to settle the patent dispute quickly.
In its lawsuit against Apple last month, Creative, known for its Nomad and Zen music players, sought an injunction and increased damages for alleged violation of its "Zen" patent.
It also sought an exclusion order and a cease-and-desist order that would prohibit the U.S. firm from selling, marketing or importing its iPod players into the United States.
According to research firm International Data Corp., Creative was ranked second after Apple in the global flash memory-based MP3 player market in 2005, with a 4.7 percent share against Apple's 16.9 percent, and was a distant number two in the hard-drive music player market with a 15.8 percent share against Apple's 72.2 percent.
Creative also competes with South Korea's Samsung Electronics , which produces the Yepp players, Japan's Sony Corp. , and South Korea's Reigncom Ltd. , whose iRiver players have won good reviews.
Mobile handset makers Nokia and Motorola are also adding MP3 functions to high-end music phones.