Apple Inc. is in talks to license music for a custom-radio service similar to the popular one operated by Pandora Media Inc., according to people familiar with the matter, in what would be a bid by the hardware maker to expand its dominance in online music.

Such services create virtual "stations" that play music similar to a song or artist of the user's choosing, either on Web browsers or smartphone apps. Like traditional radio, they are typically free for users, but incorporate advertisements.

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