By Nick Thorpe BBC News, Belgrade

The EU hopes Mr Tadic as president would tolerate its mission in Kosovo

There are nine candidates, but early results suggest a straight race between the current pro-Western President, Boris Tadic, and the leader of a hardline nationalist party, Tomislav Nikolic.

The campaign has been dominated by three key issues - the economy, closer ties to the European Union and the future of Kosovo.

Both the frontrunners oppose independence for Kosovo, but this looks inevitable.

In the next few weeks or months, ethnic Albanians in the UN-administered province are expected to declare independence.

So how will Serbia cope with that?

Imposed solution

Few people in Serbia accept the loss of Kosovo. Only one of the nine candidates in this election has publicly endorsed independence for the province.

But privately, many Serbs - and even some of their leaders - accept that Serbs and Albanians will never reach agreement on Kosovo so the only solution is an imposed one.

The next president of Serbia and the current, rather divided government, will oversee that process.

A useful barometer will be Serbia's attitude to the EU and in particular to an 1,800-strong EU law and justice mission which Brussels hopes to deploy soon to take over from the UN mission which has run the province since 1999.

If Mr Nikolic were to win this election, he could be expected to share Prime Minister Vojislav Kostunica's view that any EU mission in Kosovo without UN endorsement would be illegal and everything should be done to make life difficult for it.

If Mr Tadic wins, the EU are hopeful that an accommodation could be reached with Belgrade and that the Serbs would reluctantly tolerate EU judges and police officers in Kosovo because any border erected this year between Serbia and Kosovo will come down the day both countries join the EU.