The final judgement in the Apple Computer versus Apple Corps case is expected before the end of the month.
The Beatles holding company, Apple Corps, is hoping the case will be declared in its favour. It wants Apple Computer to cease using the Apple logo in connection with its iPod and iTunes products.
If Apple Computer fails in its defence that its service is simply data transmission, rather than the release of music, then Apple Corps will pursue the computer company for damages.
With the arguments for both sides now closed, Judge Edward Mann must now decide whether to grant an injunction barring Apple Computer from using the logo within iTunes.
Justice Mann says he will probably issue his ruling toward the end of the month, but not before Easter weekend.
Jeremy Kirk contributed to this report