LONDON — It was George Harrison--the quiet, but not-oblivious-to-trademark-law Beatle--who in 1980 first noticed the potential for conflict.

Leafing through a British magazine, Harrison saw an ad for an Apple Computer Inc. retailer. So the composer of the "Sue Me, Sue You, Blues" quickly rang up the trademark agents at the Beatles' company, Apple Corps Ltd., and asked them to investigate.

The two firms have been at odds over the name they share almost since--most recently in a London courtroom.

Apple Computer, the company that gave birth to the personal computer industry from a Cupertino, Calif., garage in 1977, and Apple Corps, set up by the Beatles in 1968 to manage their creative affairs, have passed the nine-month mark in a trademark infringement and breach of contract trial being held in Great Britain's gothic Royal Courts of Justice.

The trial, which adjourned last week for a two-month break, is not expected to end until at least December.

Apple Corps--Paul McCartney came up with the pun--filed suit against its computer namesake in February, 1989, for allegedly violating the terms of a 1981 pact that divvied up rights to the Apple name and the similar logos each uses worldwide.

A mind-boggling array of legal issues has been raised since the non-jury trial began last October. But the central question is clear: Did Apple Computer break the decade-old agreement by selling computers and other equipment used to produce music?

Under terms of the deal--struck at a time when the personal computer industry was still in its infancy and the Beatles had long since disbanded--Apple Computer would use its name and logo only in the computer business and the Beatle company would stick to entertainment.

No one, apparently, foresaw the day when computers would enter show business.

Today, Apple Computer's machines and equipment--particularly the Macintosh--are used extensively in producing, composing and synthesizing music.

"You see Macs popping up at Pink Floyd concerts and that kind of thing," says Robert DeMarzo, deputy executive editor of Computer Reseller News.

"Macintosh products are utilized day in and day out," adds Tim Finnegan, general manager of a New York outlet of the Sam Ash music store chain that is an authorized Apple dealer specializing in music-related computer systems. "It is by far the most popular computer in the recording business."