The settlement between Apple Inc. and Apple Corps offered greater hope to fans of George, Paul, John and Ringo that the two sides could now focus on permitting downloads of the band’s music through the computer company’s iTunes Music Store. The catalog of all Beatles songs, including “Let it Be”, “Get Back” and “She Loves You,” is the largest holdout from iTunes and other online services.

The two Apples have been exchanging legal salvos for 20 years over their names and fruity logos. The last skirmish came in May, when a British judge ruled that iTunes did not violate a 1991 agreement stipulating that the computer maker could keep doing business if it didn’t enter the music business. An appeal had been scheduled for this month.

The new settlement replaces the 1991 agreement and gives Apple Inc. ownership of all the trademarks related to “Apple,” meaning it could continue using its name and logos in iTunes. In addition, Apple Inc. will license certain of those trademarks back to Apple Corps for their continued use.

Each side agreed to pay its own legal costs to end the trademark lawsuit. Further terms weren’t disclosed.

“We love the Beatles, and it has been painful being at odds with them over these trademarks,” said Steve Jobs, Apple’s CEO. “It feels great to resolve this in a positive manner, and in a way that should remove the potential of further disagreements in the future.”

Neil Aspinall, manager of Apple Corps, said the company was glad to resolve the dispute.

“The years ahead are going to be very exciting times for us. We wish Apple Inc. every success and look forward to many years of peaceful co-operation with them,” he said.

The joint announcement from Apple Inc. and Apple Corps, however, was silent on the prospects of Beatles downloads.

The Beatles, who were one of the last bands to embrace CDs, haven’t allowed any online service to sell their music. Currently, the only Beatles songs for sale on iTunes are covers and tributes, and the only legal way of getting the band’s tunes onto iPods is to buy a CD and make a digital copy from that.

Long before Apple Inc. began selling music, the company then known as Apple Computer Inc. and Apple Corps agreed not to get into each other’s field of business.

Apple Corps, the guardian of the Beatles’ commercial interests, contended that Apple Inc.’s use of the logo on its popular online music store amounted to a breach of the agreement, but High Court Judge Anthony Mann disagreed in May, saying that Apple Inc.’s logo is used in association with the store _ not the music.

Lawyers for Apple Inc. had also argued that music lovers are smart enough to tell the difference between the logos. Apple Corps uses a shiny green apple as its logo, while Apple Inc. has a cartoon-like apple with a neat bite taken out.

Apple Corps was founded by the Fab Four in 1968 and still owned by Paul McCartney, Ringo Starr, the widow of John Lennon and the estate of George Harrison.

Shares of Apple Inc. fell 37 cents to $84.38 in Monday trading on the Nasdaq Stock Market.