The iPhone maker opened the stores in Hong Kong, Singapore and Taiwan.
Brunei, Cambodia, Laos, Macau, Malaysia, Philippines, Thailand, Sri Lanka and Vietnam are the other markets where the stores have been launched.
The iTunes stores would feature a selection of local and international music from all the major labels and thousands of independent labels.
Asked about the Chinese and Indian markets not being included in the launch, an Apple spokesman said, "We don't have anything further to add."
Both the Chinese and Indian markets boast a combined population of 2.5 billion with an ever growing middle-class and the world's
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