Apple Inc. (Nasdaq: APPL) and Motorola Mobility, the mobile phone-making unit of Google Inc. (Nasdaq: GOOG), lost bids for court orders barring each other from infringing their patents.

U.S. Circuit Judge Richard A. Posner in Chicago denied the requests for relief in a 38-page court order issued on June 22, ending a lawsuit started in 2010. A copy of the ruling could not immediately be obtained from the court and was provided to Bloomberg News by a Motorola Mobility spokeswoman.

“Neither party is entitled to an injunction,” Posner wrote. “Neither has shown that damages would not be an adequate remedy.”

Earlier this month, the judge rejected each company’s money-damages theories and canceled a jury trial set for June 11. “That was a simple failure of proof,” not that damages are incalculable, Posner said.

That trial would have been the first between Apple – whose iPhones are the world’s most popular line of mobile phone and Google, whose Android operating system is the world’s most-used mobile phone platform – since Google completed its $12.5 billion acquisition of Motorola Mobility last month.

Posner on June 20 heard arguments from Apple lawyers seeking an order enjoining Motorola products from infringing four of its patents, while Motorola sought an order barring Apple’s infringement of one of its cellular technology patents.

The companies also have active litigation before the International Trade Commission in Washington and in other U.S. federal courts and in Germany.

Kristin Huguet, a spokeswoman for Cupertino, California- based Apple, confirmed Posner’s ruling in a telephone interview today. She declined to comment on the court’s decision.

“We are pleased that Judge Posner formally dismissed the case against Motorola Mobility,” Jennifer Erickson, a spokeswoman for the Google unit, said today in an e-mailed statement. “As it relates to Apple’s violation of our patents, we will continue our efforts to defend our own innovation.”

Google is based in Mountain View, California.