The Beatles' record label has been told it "missed out" in the fight against piracy by failing to sign up for Apple's iTunes downloading service.
The Beatles set up Apple Corps back in 1968
London's High Court was told that the "genius" of the system is that it provides security for music.
But Apple Corps is not distributing the Beatles' back catalogue through iTunes, said Apple Computer's lawyer.
The label claims the US computer firm has breached an agreement preventing it from entering the music business.
The case is the latest in a long series of legal wrangles dating back to the 1980s when the record label took Apple Computer to court over a logo dispute.
'Very narrow use'
Apple Corps is seeking a court order to ban the computer firm from using the logo in connection with its online music store, which recently registered its one billionth internet sale.
"Apple Computer has been able to persuade every major content provider to distribute through the iTunes Music Store," said Lord Grabiner QC, acting for the US firm.
"But Apple Computer has not been able to persuade Apple Corps in relation to the Beatles catalogue," he added.
Apple Computer was founded by Steve Jobs and Steve Wozniak
The company's lawyer also argued that the case "ignored key features" of a 1991 agreement with Apple Corps, saying it is permitted to operate in a wide range of fields including processing and broadcasting.
"By contrast Apple Corps' field of use is very narrow indeed, being confined to creative works whose complete content is music," he said.
Lord Grabiner denied that Apple Computer was preventing Apple Corps from using the famous logo, and said: "They must not do their business in a way which might cause conflict with our marks."
He also claimed that Apple Corps objected to the payment made on every download from iTunes, but there was no reference to this in their agreement, calling the record label's case "inherent nonsense".
Sir Paul McCartney is credited with dreaming up the Apple Corps name
Apple Corps, owned by former Beatles stars Sir Paul McCartney and Ringo Starr and the widows of John Lennon and George Harrison, was founded in 1968.
Apple Computer, the firm whose home computers helped launch the personal computer industry, was founded in 1976.
The computer company's logo is an apple with a section removed out of the side. The record company is represented by a complete green Granny Smith apple.
An agreement between the two companies to share use of the Apple trademark was first established in 1981.
But as Apple Computer's business increasingly entered the world of entertainment, the company sought a less restrictive trademark agreement and a court battle ensued in 1989.
The case continues.