U.S.-funded radio broadcaster Voice of America said the two men worked at a Lhasa restaurant called Nyima Ling. It identified one of the men as 19-year-old Dorjee Tseten but was unable to give the name or age of the other.
"This was the first time it has happened in Lhasa — and right in the middle of Lhasa," said Tenzin Tsundue, a Tibetan poet and one of the most prominent activists living in India.
He said it reflects that anger against Chinese rule is not limited to areas where most of the immolations have occurred — the mostly ethnically Tibetan areas outside the legal boundaries of Tibet.
"All over Tibet it's the same emotion, it's the same response" to Beijing's policies, he said.
"We are always in fear of the next self-immolation, and whenever it happens we say prayers. And every time it happens we hope the world is listening."
China says Tibet has always been part of its territory, but many Tibetans say the Himalayan region was virtually independent for centuries until Chinese troops invaded in the 1950s.
Beijing blames the Dalai Lama for fanning anti-government sentiment and routinely purges monasteries and nunneries, where support for the Dalai Lama and Tibetan independence runs high.
Associated Press writer Tim Sullivan contributed to this report from New Delhi.
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