The Nation newspaper says on its website the boats were ferrying tourists to Pha-Ngan island for a "full moon" party – a monthly event that attracts mostly young Western tourists.
It says the boats collided and overturned just before midnight, throwing passengers into the sea.
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Two are reported missing and two of the 39 injured suffered serious head injuries.
Australian authorities have confirmed at least seven Australians are among the injured and they're still trying to find out if any are missing.
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