Nike has filed a patent infringement suit against Adidas-Salomon, claiming that a number of its rival's trainers copy its technology.
One of the trainers Nike accuses of using its technology
US giant Nike said the Adidas shoes in question infringed its "SHOX cushioning" patents and is demanding damages from its German competitor.
Nike, the world's largest sportswear manufacturer, claims it has 19 separate patents protecting its SHOX system.
Adidas, the second biggest, last month completed its takeover of Reebok.
It paid $3.8bn (£2.2bn) for the US firm to step up its competition with Nike and improve its market share in North America.
Adidas said on Friday afternoon that it was "currently examining the content of the complaint with our legal advisers and therefore we cannot comment any further".
"Despite Nike's patent protection, Adidas has built shoes that use Nike's technology," Nike spokesman Vada Manager said on Thursday.
Nike, which last month saw former chief executive William Perez quit after a boardroom row, has filed the legal complaint against Adidas in a Texas court.
The Adidas trainers Nike claims infringe its patents all use Adidas' a3 cushioning system, such as its new Kevin Garnett signature shoe, named after a popular US basketball player.
Mr Perez left Nike only 13 months after joining the firm and has been replaced by a Nike veteran, Mark Parker.