By Jonathan Stempel

NEW YORK, May 21 (Reuters) - Adidas ADSGn.DE, known for shoes with three parallel stripes, was sued on Wednesday by Steven Madden SHOO.O over its alleged effort to stop the American shoe company from selling fashion sneakers with two non-parallel bands.

In a complaint filed in federal court in Brooklyn, New York, Steve Madden, as the company is often known, said it has grown "tired" of Adidas' decades of complaints about footwear whose designs bear no resemblance to its three-stripe design.

These allegedly include objections to two Steve Madden sneakers launched this year: Viento, which has two bands, and Janos, whose two bands resemble the letter K.

Steve Madden said Adidas' lawyers have demanded that Viento sales be halted because the design would likely confuse consumers, and signaled to the U.S. Patent and Trademark Office it may formally challenge the Janos design.

"The use of band designs on footwear is ubiquitous in the fashion industry," Steve Madden said. "Simply put, Adidas does not own all stripes and should not be allowed to claim that it has a monopoly on all footwear that includes stripes, bars, bands or any shape having four sides—parallel, straight or not."

Adidas did not immediately respond to requests for comment outside business hours.

Like some shoe companies including Nike NKE.N, Adidas sometimes turns to U.S. courts and agencies to stop rivals from selling products it considers knockoffs.

Steve Madden, based in Long Island City, New York, said Adidas sued it twice in 2002 to challenge footwear with two parallel stripes and four parallel stripes, leading to a confidential settlement the next year.

The latest dispute does not arise from that accord.

Wednesday's lawsuit seeks a judgment that the Viento and Janos designs do not infringe Adidas' trademarks or three-stripe design, allowing Steve Madden to continue sales.

The case is Steven Madden Ltd v Adidas AG et al, U.S. District Court, Eastern District of New York, No. 25-02847.

(Reporting by Jonathan Stempel in New York; Editing by Leslie Adler)

((jon.stempel@thomsonreuters.com; +1 646 223 6317; Reuters Messaging: jon.stempel.thomsonreuters.com@reuters.net))