Two new trademark infringement suits were recently filed involving celebrities.

Clothing company L.A. Triumph filed suit against Madonna and her recently launched Material Girl brand fashion line, arguing that her use of the “Material Girl” mark infringed its registered trademark and that consumer confusion has already occurred.

In the second suit, George Lucas’s Lucasfilm alleged that software maker Jedi Mind, Inc., was illegally using the “Jedi” marks to sell a wireless headset that claims it can detect brain waves to allow users to run software or play games using their thoughts.

In California federal court, L.A. Triumph claims that it began selling a “Material Girl” line of clothes for teens in nationwide department stores in 1997, while Madonna’s line – which her 13-year-old daughter, Lourdes, helped produce – just launched in August. The company even filed a trademark registration with the state of California, according to the complaint. L.A. Triumph is seeking a declaration that it has senior rights to the “Material Girl” mark as well as actual damages and any profits attributable to Madonna’s use of the mark.

In the second suit, Star Wars mastermind George Lucas challenged a company that attempted to sell software that allegedly allowed users to control their computers with their thoughts. Lucasfilm Ltd. filed suit in early August against Jedi Mind, Inc., a company that offers “computer applications, controlled by a wireless technology which is in turn controlled directly by the user’s mind, without the need for a joystick, Wii or other physically manipulated control device,” according to the complaint.

Noting that the Jedi mark has been “known globally for almost 35 years as a reference to the powerful, knowledgeable, brave and (usually) good-hearted science fiction warriors known as Jedi knights,” Lucasfilm sought $5 million and treble damages for trademark infringement.

Despite Lucasfilm sending two cease and desist letters, Jedi Mind, Inc., began offering three products for sale in July: “Master Mind,” “Jedi Mouse,” and “Think Tac Toe.”

The Force was apparently with Lucasfilm, which already received a permanent injunction against Jedi Mind, preventing it from using any of the production company’s trademarks – including Jedi, The Force, and Jedi Mind Trick – and mandating that it change the name of the company and its products. Further, U.S. District Court Judge Charles R. Breyer ordered existing infringing materials to be destroyed, possession of the company’s domain name turned over to Lucas, and that the defendants pay $250,000 in damages.

To read the complaint in L.A. Triumph v. Madonna, click here.

To read the injunction in Lucasfilm v. Jedi Mind, Inc., click here.

Why it matters: The lawsuits are a reminder that celebrities with intellectual property rights can find themselves on either side of the bar.