International organisers hope to see moderates who accept the American- brokered 1995 Dayton accords that ended the 1992-5 war gain strength at the expense of separatist hardliners.
The Organisation for Security and Co-operation in Europe which is running the elections, estimated a turnout of 70 to 80 per cent.
But even before the results are known there is concern about what they will mean for Bosnia.
Peter Palmer, an analyst,said: "Moderate nationalists will make progress, but they are still nationalists." Without some way of getting people to think beyond their ethnic identity, the West would need to be present in Bosnia for a long time to come, he added.
The former Bosnian Serb leader Radodan Karadzic is still at large in Bosnia, wanted by the UN for alleged war crimes.
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