Some 6.5 million voters are choosing the president, a new parliament and local authorities in the capital, Belgrade, and over a dozen other towns and municipalities.
The ballot focuses on changes in the election of judges and prosecutors that authorities say are aimed at boosting their independence in the country.
The French court ordered the immediate release of Ramush Haradinaj, accused by Serbia of war crimes.
Conservative Prime Minister Aleksandar Vucic is the runaway favourite to win Serbia's presidential elections while the opposition has been unable to field a united candidate to run against him.
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