Voters are choosing deputies for the two autonomous regions - the Muslim-Croat Federation of Bosnia and the Bosnian Serb Republic - which were set up under the 1995 Dayton peace accord.
About 2.75 million Bosnians are registered to vote for a tripartite presidency and central parliament, choosing from 36 parties, eight coalitions and 12 independent candidates.
Polling stations opened at 7am (0500 GMT) across the country and will close at 7pm (1700 GMT).
First preliminary results for the presidency are expected late on Sunday and for the other electoral races on Monday.
Most Muslim parties oppose the existence of two autonomous regions, claiming that the Serb Republic was founded on ethnic cleansing and that Bosnia can never become a viable state if one half demands a separate identity.
Croat parties want effective protection of their distinct rights, with some tentative calls to create a third entity.
Most Serb Republic parties stand for preserving autonomy and oppose the creation of a single police force, which came into effect late last year, a key EU demand for advancing Bosnia's membership bid.
Each region has its own president, government, parliament, police and other bodies.
Overarching these entities is a central Bosnian government and rotating presidency.
The Dayton accord has been criticised for creating two separate states and for fuelling nationalism, but it has brought some stability to Bosnia.
A breakthrough came last year when a single defence structure and intelligence service, a central judicial system and a single customs service were created.
Opinion polls in Bosnia are not reliable. However, in the Serb Republic some have indicated that the Party of Independent Social Democrats (SNSD), which is led by Milorad Dodik, the Serbian prime minister, will win a resounding victory.
Two-time leader Dodik has launched an ambitious economic recovery plan since taking office in February.