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8 year oldJean Ping, ex-head of the African Union commission, said he was waiting for the president to call and congratulate him.
Mr Bongo, whose family has governed for nearly 50 years, has called for calm and for people to wait for official results on Tuesday.
Gabon is a major oil producer, but still has high levels of poverty.
The head of the African Union election observer mission in Gabon, Casam Uteem told BBC Focus on Africa that he was not worried by the uncertainty.
"So long as as the results are not made official, I don't think anybody can claim victory at this stage," he said.
The atmosphere in the capital Libreville was calm overnight, according to a BBC correspondent on the ground.
Ali Bongo won disputed elections in 2009, following the death of his father Omar Bongo, who led the small West African nation for 41 years.
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