According to diplomatic sources, the voter registration numbers in Brcko municipality slightly favour the Muslims and their nationalist party, the SDA. A Muslim victory would have dramatic consequences, as Brcko lies in the narrow corridor linking the northern and eastern halves of the so-called Republika Srpska, the Serb-controlled half of Bosnia. Its status has been in dispute ever since the end of the war, and is currently under the control of an International Supervisor.
The two days of voting might spill over into today and results are not due to be published until later this week.
Brcko is now occupied entirely by Serbs, many of them refugees from other parts of the former Yugoslavia. A Muslim victory would put pressure on the Serb refugees to leave the town and further squeeze the Republika Srpska's precious corridor. Whoever wins, there is sure to be an ugly confrontation between the evenly balanced numbers of new municipal councillors.
Brcko is one of a number of municipalities where the pattern of ethnic purity established by the ceasefire and the signing of the Dayton peace agreement two years ago promises to be upset by the elections.
Serbs are almost certain to take control of Drvar, a town in western Bosnia now held by Croats, and are likely to put in a strong performance in the neighbouring town of Glamoc, the diplomatic sources said.
In Serb-held eastern Bosnia, scene of some of the worst atrocities against Muslims of the war, the SDA is looking strong in such towns as Foca and Visegrad.
The elections, which have been run entirely by the international community, have been deliberately weighted to give a stronger voice to refugees who were forced to leave their homes during the war. Voters could choose to vote either in their 1991 place of residence or in their new homes. They did not need to fear returning to a hostile area for the election itself because they were free to opt for an absentee ballot.
It is far from clear how ethnically anomalous election results can be enforced.
In Mostar, where test-case elections were held in June 1996, progress in persuading the rival Muslim and Croat factions to work together in the same city hall have been painfully slow and the city remains deeply divided.
Diplomats are vague about how to avoid creating lots of mini-Mostars all over Bosnia. They hope to put pressure on the politicians through the threat of economic sanctions, but are not sure how to sway ordinary citizens, who mostly oppose a return to multi-ethnic living. The elections passed off remarkably quietly at the weekend, with one report of violence. But events in the town of Drvar gave a taste of the possible problems to come.
About 1,000 Serbs, organised by the Banja Luka-based party For Drvar, decided to return to their former home town to cast their ballots, but were held up for hours - first by Croat police who tried to slow them down on the road, and then by Croat election officials who deliberately chose to put them through the voting process as slowly as possible.
International authorities were forced to provide blankets and tents for the Serbs on Saturday night, and set up a mobile polling station yesterday to help them exercise their democratic rights.
A spokesman for the Organisation for Security and Cooperation in Europe, Johan Verheyden, called the Croats' behaviour "despicable" but vowed to keep the polls open long enough for all the Serbs to vote as planned.
Sarajevo - A Bosnian opposition party member was shot and wounded around midnight on Saturday while on the way to inform authorities he was being harassed by the SDA, Reuters reports.